It's how most of the rest of the world works.

Is this not common in America?

It used to be and there's been a push to get back to it. I think City Journal, major conservative/libertarian group, has been writing about it.

It basically went away with modern zoning laws.

It's fairly uncommon, yeah. Often it'll be allowed in a smallish 'downtown' area and nowhere else, so most of the city isn't very walkable in terms of doing errands.