Where I grew up, a town of about 10,000 people, the total extent of "public transit" was a van service that served the elderly and disabled.
That's called public transit assuming anyone can use it, which is the way it works most places. If you mean scheduled bus service, then yes that is more limited in both suburbs and rural areas where it exists at all.
Wow. I looked it up, and today I learned that it actually is available to non-seniors. I'm kind of surprised. Of course, the median wait time is measured in significant fractions of an hour, so even the elderly prefer to get rides from other people when they can. Either way, there's no advantage to a van that drives around and picks up one or two people at a time and takes them to their destination compared with a private car (and actually a huge disadvantage from a fuel economy perspective). It's just a glorified Über service, but with the most fuel-inefficient vehicles on the road.
I'm talking about small town USA.
One of the firm criteria of our choosing our house was that it be within walking distance of work and a grocery store. We didn't even look at houses that didn't meet that criteria. Did that mean we couldn't have five acre spread in the woods? Yes. Did it mean we couldn't live on a lake? Yes, we couldn't afford lake front property that met that criteria. What I am talking about is what is real, not your imaginary small town.
My actual small town that I lived in until I was 22 currently has almost no houses within a twenty minute walk of any of the grocery stores. Maybe a few of the houses closest to the front of one of the wealthiest neighborhoods are close enough to Walmart. E.W. James (oops, that apparently just became a Save-A-Lot) is on a highway with almost no houses for probably a mile. Ruler Foods is within a mile of maybe a half dozen houses.
The Big Star store that went under in the 1980s (IIRC) was within walking distance of maybe a dozen mostly low-income houses, plus some university married student apartments, and *barely* within walking distance of some of the other university housing, but that has been gone for decades. The old E.W.'s was within walking distance of maybe low-double-digit houses before it moved across town in the late 1990s to where Ruler is now, and then again to its current location. IGA was also kind of near some houses, but again, that closed in the 80s or 90s when all the businesses moved to the west side of town to be near Walmart after it moved.
But even if you distributed them as evenly as you could, with only three real grocery stores, you'd still only have maybe 10% to 15% of residents within a reasonable walking distance of a grocery store. At 850 people per square mile, you just can't sustain a lot of grocery stores. And that's before you factor in all the people out in the country. For that matter, my current city has trouble keeping more than about three grocery stores in business at anything approaching *bikeable* distances even with 7k people per square mile. The economies of scale just lend themselves to a smaller number of larger grocery stores, rather than a larger number of smaller stores.
trying to eliminate cars can't work in rural areas,
I agree and lowering the speed limit doesn't eliminate cars. It reduces their emissions immediately instead of waiting 20 or 30 or 40 years when the only cars on the road are electric.
Except that this isn't true. Yes, above a certain speed, you rapidly lose energy from wind resistance. But at lower speeds, you're not getting the maximum advantage of higher gears. That's why most cars are more efficient at 55 to 60 MPH than at 40 MPH. So lowering the maximum speed will NOT necessarily reduce emissions.
Here's a graph of a few vehicles' efficiency versus speed. Going significantly over 60 MPH usually results in a significant reduction in efficiency. Below that, though, you're just as likely to make emissions worse by slowing people down as you are to make it better. It depends entirely on what speeds just happen to be at the sweet spot in the torque curve of a particular engine with a particular gear ratio. You really can't fix the environment with that approach. All you'll do is make people late all the time.