Horse and cart, no. But some cities have banned cars and replaced them with various alternatives, and it works.
There are alternatives to the car culture we have. It would require significantly rebuilding how we build infrastructure, but the result could be much safer, cleaner, and less stressful.
Of course Americans would rather die, but counties of sane people might be able to work it out.
> It would require significantly rebuilding how we build infrastructure
That simple huh?!