What you state as "urban sprawl" would be "mostly normal" living density for a city like Rome. When I walk the streets of larger cities, its not like the downtown core has acres of land per house, or even a 1/4 acre.
Now of course, there are some differences over time. But my point is that it's not as if the car has caused urban sprawl, in fact, downtown cities are far more dense than 500 years ago. Or 2000, or whatever. One 40 story apartment building, which is common not even just in downtown cores, is a lot more dense than anything 1000 years ago, land use would be 10x or 20x or even 40x.
I know there's this fad to pretend the car caused every problem ever, but it's just not true.