s/too happy/required to/
Try to get by with a high-earning single income in the south bay area or a median income in any metro. Housing prices and health costs force families to move to dual income.
Still, in my calculus, the benefits outweigh the risks. Here's another anecdote:
Once a week my kids get together with several other home-schooled families. In one of those families, the father is a math professor at the local community college. He's smart. He could work at any of a number of universities and make better money, but he's chosen to work at a community college because it gives him a more flexible schedule to be around to raise/educate his children.
His family of 7 lives in an 1000 sqft home. His decision to take an active role in educating his children required sacrifices, and he's chosen to trade off the career benefits for home life benefits.
(BTW, when people talk about "diversity", this is the kind I think that matters most. Diversity of viewpoints on how to live your life and raise your children. I'm glad in the US we don't have to all agree on the best way to do these things.)
You might find it to be a better life (I don't) but it's not more sustainable.
Small town with car: go a few blocks, never stopping for traffic, going the direction you like and stopping where you please
Big city with car: go many blocks, constantly stopping in traffic, route around 1-way streets, and then slowly loop around looking for a place to park
Big city with bus: go many blocks, constantly stopping in traffic, route around 1-way streets, often going kind of the wrong direction, spewing diesel soot all the way -- and often the bus runs nearly empty, a big soot-spewing vehicle with almost no people
That's obviously not all city transit but it's a much larger part. Also lots of grocery stores still have parking lots (actually garages) in the city. If you're going somewhere like that you can still park easily. Depends on the location I'm sure.
I'm not sure what your dislike of buses is. They are far more efficient than personal transit from a fuel perspective. A bus can be "nearly empty" and still replace a half dozen cars. And at peak times a bus will replace dozens. There are issues with buses but "soot-spewing" isn't one of them, at least not relative to cars.
Small town is also not really country. If you can drive a few blocks to the grocery store, you don't live in the country. In fact, if your house is near blocks, you don't live in the country. Small towns are of course also less sustainable than cities as small towns are basically built like suburbs.
You're assuming city life and country life are largely the same. In the country you don't pop down to the market 3-4 times a week when you run out of milk or want to grab a sandwich -- you buy a deep freeze and go "big shopping" once every week or two.
What IS nice is that the car time tends to be long like you said, 20 minutes, 40 minutes, which is more efficient energy-wise and for wear and tear than a bunch of little 5 minute trips.
You have to live a place that's right for you. I'm perfectly fine not leaving the house for days on end, there's plenty to do around here. Some of my friends would go crazy if they didn't have someplace to go every night. If you're the latter kind of person, country living is probably not going to agree with you! The same is true vice versa -- how do I go to Costco on my bike!? ;)
You'd do better to gather more information on the topic.
It's possible that when the data refers to two parents in the labor force it means that both parents are employable, as opposed to employed. That doesn't make sense to me, however, as it would indicate that half of non-homeschooled families have only one employable parent. Unfortunately, I don't currently have the time to drill down into the raw data to investigate the definition they used.
https://www.census.gov/prod/2011pubs/12statab/educ.pdf (Table 240)
Seems like a stretch of the terminology to call it "homeschooling".