Putting aside that I’ve seen some relatively old people continue to stay healthy on bikes (often as leisure, not utility), generally the hope would be that public transit would cover the needs for longer distances. As you said, many current forms are pretty bad, but that’s because our money is spent (that is KEY - we SPEND the money either way!!) on road maintenance and new parking garages, and of course individually on car maintenance.
We also have these long distances to cover to stores in part because of the big wide roads and parking lots that elongate our trips. As it turns out, civic centers don’t have to be so spread out.
I’d also expect most people not to need to go into the city for all forms of shopping. If you just need groceries for the week, but your town has nothing to offer in walking distance, it almost sounds like there’s a business begging to be built there, even if it’s a two-room local affair.