Don't know why I want to feed the troll -- and explicitly not accepting the assertions I don't challenge here, but...
You talk about "traffic flow" -- but think about this for a minute. You're proposing to take a very high-population, dense chunk of city -- plugged into the rest of that city's transportation network -- and move it out into the middle of nowhere.
Have you looked at the level of car ownership in high-density areas recently -- particularly in lower-income high-density areas? How exactly do you expect folks to get to work or school when they're suddenly no longer in an area with transit access? (And without that, how do you expect folks to work, or go to school to improve their circumstances? Would you rather be buying the same number of heads worth of homeless shelter, and getting no tax base at all)?
Hell. I'm in the rich part (financial district) of downtown Chicago, and less than half my neighbors if that own cars if that; being in walking distance from work (and directly next to a stop for every single L line) is why people pay to live in the Loop. Owning a vehicle is expensive in a city -- heck, parking wherever you're going to is expensive in and of itself, as is having a place to park that vehicle at home (in my building, a parking spot costs about $30k to buy, or rents for upward of $200/mo). You can't take folks who can't afford decent housing unassisted, move them away from their jobs, and expect them all to be able to buy, maintain and fuel vehicles -- and park those vehicles near their jobs in the city -- when they were only barely making ends meet beforehand. It's insane.