Fundamental characteristic of sprawl is not, as often mooted, low density. Many naturally occurring places are low density. Rather, it is the segregation of uses that most characterizes sprawl, and is the most problematic element of sprawl, for it is what causes the most problematic outcome of sprawl: An excessive amount of driving.
It is the separation between home and work that is the problem. Separation means distances are greater. This reduces the viability of active transport (walking, biking), and also reduces the efficiency of transit.
Perhaps things would be different if housing and employment were clustered near transit stops. But they are not--while employment is naturally concentrated in a limited land area, in a limited number of establishments, housing is dispersed across a wide area. This dispersion of housing should not be considered natural, but unnatural--it is the result of a politically determined, rigorously policed, and financially subsidized [1].
The argument is not that people would choose a higher density, but rather people would accept a higher density if it meant a shorter commuter or lower rent. The present circumstance denies the opportunity to make this decision.
The essence of a city is to minimize transportation costs through co-location of economic activity. Correspondingly, all cities in history located where transportation costs were lowest--ports, rivers, crossroads. Everything else is a 'town' - a central nub of services for the surrounding area.
Let's stop talking about the suburb as cities. They aren't. Suburbs are highly concentrated hamlets--clusters of housing. Clusters of shops spring up to serve them, acting as main streets and high streets once did. Unlike naturally occurring towns, the employees and their families don't live in down, but in the hamlets near town. Why? Because they have to--the separation of use obliges them to and forbids the mix of use. No 'live-work' units are legal.
Sprawl is problematic because of the separation of uses, which increases the distance required to travel and thereby induces auto-dependence. Auto-dependence begets auto-use, which begets traffic congestion. Efforts to reduce traffic congestion by increasing capacity (in both roadways and parking lots) further reduce average density, increase average travel distances, and further reinforce auto-dependence. And so on, in a doom loop.
However, there is a long-term twist to this doom loop: At some point, the land-use efficiency drops below the level where the taxable value that can be extracted from the land is less than the maintenance cost of the system: maintaining roadways. (Highways are another story--most highways are funded at a state/federal level. Hence there is no need for a locality to be functional to maintain them--value can be shifted from somewhere else, via the gas tax.)
Throughout history, population and employment have been co-located; a human can only commute so far in a day. Empirical work suggests this averages about half an hour a day, each way [3]. Hence, a mono-centric city can only be so large. Lot coverage can only be increased so far--multi-level structures become feasible with surprisingly low population densities, as evinced by split-level suburban homes. But structures can only go so high--masonry buildings top out at something like 10 stories, and the additional cost of a vertical climb means almost nothing taller than 6 stories has ever been worth it without elevators. That the highest stories once had the lowest rents is telling--as is the "Belle etage' of an elevated first floor as the ideal.
Separation of uses induces unnecessary travel. Splitting work from home means people must travel further. While the original buyer may have been pleased with the change and been willing to travel 10 minutes more for twice the house, every succeeding resident has been stuck with that decision. And will be stuck, because housing is durable and we've made redevelopment impossible. Everyone wants a detached house, but everyone wants a pony too. But surprisingly few people are willing to pay for ponies and may decide their lives are better off with some other transportation alternative. The presumed inevitability of the enduring nature of sprawl comes from the systematic elimination of alternatives. This is why things like the triplexes, backyard duplexes, etc are so shocking (and so freeing) because they reveal that the current context is only as fixed as we choose to make it.
Until we make the choice to permit our urban environment to change, to let density increase in concordance with the increased demand for it, all our transportation choices and mobility alternative experiments are just tinkering, and not enough to move the needle.
Ironically, as an urban planner, I hate Euclidian zoning. As an urbanist, it's almost natural. The best places aren't zoned. Regulated, yes. But never in the American '11 different types of residential zone' flavor. I hear tell Japan has a national zoning code, with a limited number of zones. I admit some jealously and wish more of our states would follow suit.
Low density is a product of sprawl, rather than a cause of sprawl. Left alone, any amount of sprawling development would naturally densify, developing a radial polycentric form with a single primary center and manifest radiations of secondary and tertiary sub-centers. Start with a uniform field of homes (and uniform streets) and watch it emerge. More central paths are used more often. At some point, a congestion equilibrium is reached. Some arbitrarily widened paths, with lower congestion, will receive more traffic, drawing additional traffic through it's tributaries until the same equilibrium is reached. Correspondingly, any business devoted to selling things to other human beings (goods/services) will also concentrate along high-traffic paths, simply to maximize exposure to customers. And the wealthier occupants of said shops will locate at an equilibrium location that is close enough to commute, but maximally distant from the nuisance (pollution and noise) of said traffic. The wealthier you get, the more space you will take up, and the more effectively you will buffer yourself from other people. Given infinite resources (and teleporter booths), we would have had private demi-planes and space habitats. But until the transportation is both free and frictionless, locational preferences will be weighted against transportation costs.
I don't want everything to be different: I want the option for different places to do different things. And the imposition of uniformity (via state and federal highway regulations) is contrary to that. Easy to claim I've let my preferences inform my ethics, and that other people like the way things are just fine. To which I can only respond: Accepting what appears to be unchangeable is very much the opposite of choice: offering chocolate is not a choice. Offering chocolate and imitation chocolate is not a choice, nor is luxury reserve chocolate and basic chocolate. Offer even the whiff of strawberry, and see if people still want chocolate.
But, back to sprawl: separating uses results in increasing travel distances, which results in increasing auto dependence, which necessitates devoting more and more land area to automobility (primarily parking). Ensuring the sufficiency of ROW demands enormous public expenditure, leveraged through a regressive gas tax. Ensuring sufficiency of parking places a burden on any hopeful business; making re-using an existing site a nightmare---an angle I had not considered. In addition to its burdens of ROW and parking, sprawl also destructively idles vast tracts of land between their initial use and when land-rents support multi-level parking structures. Certainly, there are interim uses, but they are marginal: the original structure was efficiently designed only for the first tenant: and later tenants face a deadweight of excess parking (prospective tenants with parking needs to be judged in excess of existing supply being regulatorily prevented from coming into operation).
Element not heretofore explored: We have spoken of people and jobs as one class. This is nonsense. Different people make different amounts of money. Even assuming an initial random assignment of agents with different home and workplace locations, sorting would follow, as agents moved between homes like hermit crabs between shells, chasing vacancies in such a way as to reduce commutes. (A simplification, ignoring nuisances and presuming each house is identical and can be fixed up/decorated to match the owner's income/wealth level). For the sake of a thought experiment, let us assume 3 general classes (as the American Community Survey does), and call them poor, middle-class and wealthy, with each class able to outbid the prior for locations. Hence, if a vacancy emerges, a wealthy household gets 'dibs' and rights of first refusal, and the poor have to make do with whatever locations not previously selected. In a nuisance-free context, those locations will be the worst, most peripheral, and least accessible locations.
Group selection is another wrinkle--assume that people like to live next to people of their own class-similar mores, customs, affordances, rituals, etc, reducing the nuisance of living in proximity to others--if they are obstreperous, they are at least so in ways you judge understandable. While there is some claim the less wealthy would like to live next to the wealthy, this is a nuisance issue--the poor seeking to avoid the ills of poverty. Living next to next-class-up is unwelcome--the middle-class are always calling the cops on the poor, and the wealthy are always siccing their lawyers on the middle-class. Which is, in its own way, a nuisance issue.
This aside: poor in most peripheral locations; wealthy in most central. Wealthy will probably also maintain an exurban, extremely non-central location. The more wealthy, the more comfortable it will be, and the longer they will be able to stay there. The minimal threshold would be skipping out for the weekend, the maximal threshold would be having a 'summer home' or multiple seasonal homes to rotate among.
Employment always remains concentrated. While there may be multiple workers per household, the average number of persons/business establishments is much higher. So the ratio will always be higher for businesses, simply because businesses scale in a way that households do not--they need not rely on the natural increase to grow larger. The business also benefits from returns to scale on capital goods--gets more use (time-efficient) out of each needle, but also are able to spread the wagon over more users (cost efficient). But biz also often more space efficient: space/worker is typically lower than space/person (highly industry dependent). Further, households have non-worker dependents (children, sick, old). The rule of thumb I recall was there was a 5:2 ratio of population to employment. So assume a 5:2 ratio of space for households vs. space for business establishments.
Sprawl is polycentric. This emerges two ways: Urban agglomeration, as existing urban centers become conjoined through expansion, and sub-center development, resulting from Christallier's [2] urban hierarchy.
[1] The Color of law; others.
[2] Von Thunen also; Alonso, Mills, Muth.
[3] Marchetti's constant