In the cities, where nobody really lives in the historical center, it is doable. (We are not talking about driving through; we are talking about access/servicing; there are very few cities without a ring -- or several rings -- where driving through center is the fastest way from one end to another).
In the cities, where real people live there, it is not. Every part of the city needs servicing, including center. Your plumber won't lug his tools on a scooter; your furniture won't teleport itself into your house either. Every now and then, the residents themselves need to bring in or out their heavier or larger crap, so issuing permits to entry to well-connected companies is not a solution.
Yes, I do live in city center; and yes, we also have people who know nothing about living there, but they go to pub there every Saturday night, so they have strong ideas how it should be. It is not limiting them, after all.