So, in addition to "affordable" housing, in your ideal world, the poor will also be provided (by someone) with "affordable" Priuses?
Perhaps you've heard of this thing called "transit"?
Which, when done right, gets used by everyone, not just the poor. It was not so long ago a culture shock for me, as a Texan, when my (New-York-based) CEO would take the subway; now, as a transplant to Chicago, I'm very much happier not owning a car at all; my work is a 10-minute walk (hooray for urban high-rise living!), Costco a 20-minute bike ride (hooray for cargo bikes!), my more distant friends in town (or the corporate office, if I need to visit it for some reason) a $2.50, 40-minute train ride, during which my time is free to read, make notes, or otherwise do as I please.
Back to point -- no, setting up your urban environment in such a way that the poor need to drive expensive-to-maintain, expensive-to-fuel vehicles a long distance is not a necessity. Transit systems are subsidized at a higher rate than roads, but not by as much as you might think -- use taxes on highways are under 50% of their costs -- and adding capacity to a roadway system in an urban environment is prohibitively expensive -- particularly compared to adding capacity to preexisting urban rail. And if you look at the economic payoff from that subsidy -- by way of increasing folks' access to jobs -- it's an extremely clear win.
Smart urban planning -- to avoid the need for commutes in the first place by making housing as dense, and nearby to shopping and employment, as possible -- is, of course, even better.
(Back on the "expensive" part of long commutes -- you might find The True Cost of Commuting a worthwhile read, in terms of putting some actual numbers into play).