I'm really doubting this is the case. It seems much more likely to be due to zoning laws.
And further why are zoning laws the way they are? It's exactly because the suburbs people don't want a bunch of hippie trailer park riffraff around.
What if it's both? People drive everywhere because zoning forces car infrastructure everywhere. There's few to no safe places to walk/bike anymore.
It's not really.
If you have cheap, abundant land it makes no sense to build densely.
Look at Houston with ~zero zoning laws and ~infinite sprawl.
"A neighborhood" in a high-sprawl suburb wouldn't be able to support local mixed use amenities because even singular "neighborhoods" are gigantic enough to warrant driving across them. Once you're in the car, why would you go to the place 2min down the road instead of the far superior place 8min down the road.