Back in the day, before cars were widespread, everything had to be close by.
You don't even have to sacrifice the backyard for that, you can have a city layout that puts the houses themselves fairly close to each other, and the yards can radiate outwards. Then you connect each cluster's main street with the other ones, but unlike suburbs, you make each "subdivision" mixed-use and you allow public transit , pedestrians and cyclists to cut across subdivisions for easy access everywhere.
If anything, small towns should be urbanism done right, because they don't (shouldn't?) have the money for sprawl and they don't have all the pressures for increasing density a lot, that big cities have.
My grandparents, and their parents and grandparents before them, all grew up on farms (as did the majority of Americans during that time).
No, everything did not have to be close by.
They certainly did appreciate cars when they became affordable though.
In most of the world villages have at least a cluster of homes nearby, since having other humans close is super handy when shit hits the fan.
Yes, these are the rural areas of which we speak. Everything gets spread out and then you're stuck travelling long distances to do anything, just like those who live in actual rural areas. There is no question that transportation is necessary in a rural area.
A proper urban environment, however, puts everything right there in a short distance. No need to ever travel beyond where your feet can take you. That's the whole reason for living so close to other people.
But it's clear that people want to live in (or pretend to live in) rural areas. It seems to be in our nature. As such, there is a lot of pressure to maintain the way things are. Hence the ill-conceived cries for better transportation to maintain the rural way of life instead of actually embracing urbanity.
If cars simply didn't exist, our cities would not, could never have, been designed the way they are, in any way.
Nah. Many cities long predate the car. They absolutely were designed in the same way they are still found now, aside from what are now roads were squares for people to walk in. Return the road back to being a square and nobody would be able to recognize that there was a car era. But, so long as the people want to live a rural lifestyle, good luck…