If by "personal vehicles" you mean mobility scooters and wheelchairs, then sure!
Nobody should actually need personal automobiles in a properly-designed city, though. Not even disabled people. The only kinds of automobile traffic that are actually necessary should be deliveries, tradespeople, and buses.
Okay, but when a properly-designed town looks like this...
...it's not as if they'd have anywhere to park their van anyway. The correct solution here is to have plentiful public seating for them to rest on and for them to pull their equipment along behind them in a cart or something.
Your argument is as unreasonable as suggesting they should be allowed to drive through an indoor shopping mall, Blues Brothers-style.
16th Street in Denver is just that, one street. And it's really only like that for about 8 blocks. It works fairly well to build in that way for a small area but replacing all of the downtown infrastructure is not really practical, much less the whole city.
Amsterdam is about the same size as Denver and has a at least low car city center. Works pretty well.Venice down town might be one of the most beautiful in the world and is pretty much completly car free. It sort of works, besides the tourists that is.