Other people who also self-identity as ME matter too. THEY will still welcome YOU. absent the brum-brum which, in aggregate with other brum-brums, is a massive annoyance to THEM.
Depends on the downtown area.
If there is enough population living within walking distance of the shops to sustain those shops then the businesses will be fine. And the area will be more pleasant for those who do live within that area, so that's nice. It does become exclusionary for those who live outside the area as parent poster said but perhaps that's ok, as long as the population density there is high enough to keep it going.
But many downtown shop areas don't have enough population within walking distance to keep the businesses viable. Those areas depend on people from farther out driving in to spend their money. For those, making parking difficult (too far, too expensive) can quickly go into a downward spiral of shops closing, area decaying, becoming less attractive to visit, leading to even more shops closing, until the old downtown core is a ghost town.
So population density is key. If density isn't there one can't just slap a prohibition on cars/parking and expect it to work well.