I live in a small suburban city and I can walk to:
* The library (5 minutes)
* A supermarket (8 minutes)
* A dozen restaurants (7-15 minutes; mostly local restaurants + 2 fast food chains)
* Two liquor stores
* A drug store (12 minutes)
* A coworking space (15 minutes)
* Several antique stores (12-15 minutes)
* (Almost forgot) Walmart (10 minutes)
* Two barbers (8-12 minutes)
* At least three major bus lines
And if I get on a bike, I can go across the entire town in 20 minutes, which puts me in range of more supermarkets, a local game store, a Gamestop, a bowling alley, at least two dozen more restaurants, and tons more.
There are places to live in my town that I would be stuck driving (or at least biking) everywhere. But I chose a place near the downtown area, and I can walk to tons of places. And I do.
Not fond of big cities. My kids can wander around my neighborhood or walk to the park, and we don't worry at all. Granted it's not six miles to the park. Six miles in any direction and you've left the small city I live in. But we're trying to resist the helicopter parenting style.
That said, I think there's another thing that's missing from this discussion: People are having fewer kids. Sometimes they have a single kid. So it's natural when all your eggs are in one basket to be a bit more paranoid about that basket.