I'd rather have fifteen minute service every half mile then thirty minute service every quarter mile. Its worth the walk to save the wait. In an urban environment, I walk a 20 minute mile so an extra quarter mile is an extra five minutes. Five minutes of walking to save fifteen minutes of waiting? Sign me up!
But what about seven minute service every mile? Tempting, but I don't think it's worth it. Another half mile is 10 minutes of walking, while the doubled headway will only save me, at most, 7 minutes.
As a transit dependent renter, proximity to transit is my #1 search criteria. Two blocks (1/4 mile) was simply too far to walk every time I want to go someplace. I don't even look at apartments outside that radius. On that basis, a network of transit lines every half mile provides service to every location.
Not everyone is as able as I-- the old, the infirm, children, and young women have a harder time of it. But I would argue that for the first two, the lack of seating while waiting is actually harder then the walking. And for the latter, I think the wait at the bus stop is the most vulnerable part of the trip.