Sure, on your own land, just like you can drive more-or-less whatever you want as long as you stick to your own property, today, including vehicles that aren't "street legal".

On public roads? No reason we'd have to license private cars for that, at least not for just any purpose.

How about the fact that any country that tries to ban private ownership of cars would completely fall behind in all car-related technologies, infrastructure and services, which would very soon negatively affect all those commercial or logistical use cases that our civilization vitally depends on?

Trying to ban all private cars while keeping our car-dependent civilization working is unrealistic, no matter how you look at it.