I grew up from 10 to 18 in a moderately rural area outside of Dallas. We share fine if and when we have to, but for the most part, we don't have to.
I saw a lady walking along the side of a rural road - this was about 12 years ago, so there weren't buses then, and there won't be in the next 12 years either - so I pulled over and asked her where she was going. Turns out she was going to walk, in the summer heat, to a grocery store about 10 miles away.
We shared my car just fine. But I certainly wouldn't go over to a neighbor and ask for a ride to the grocery store if my car was running ok.
I think that's it. Needing to share or using someone else's car is seen as a sign of weakness. OK for an old lady maybe. But a Real American rides their own damn car, and pays for their own damn healthcare...
I think it's actually because the USA has 0.8 cars per person. Why would people carpool or rideshare in a rural area when they've more-than-likely got their own cars?
But maybe, yeah..