Problem for elderly and sick people who need cars to get around.
And if people start abusing that, at least their relatives or random elderly people get out and about for more sightseeing!
I know it causes issues. Not saying it can't be solved, but it is naive to say that simply banning cars is always a net plus. Why did people living in the city even buy cars to begin with?
My father used to be a doctor in a place that got converted into a pedestrians only area, he reported that a lot of people had issues. Business for other shops also declined.