Leaving aside that neither groceries or medical services are free, the problem isn't that parking will now cost something. There won't be enough parking to go around and many people will be entirely priced out. People will be unable to park near the services they need and many will have no place to park/charge the cars they still require at the end of the day when they're at home.

That's not a good situation for anyone except for a very small number of people who will make more money than they have been, and small number of already wealthy people who will find lots of available parking they can easily afford now that they don't have to compete with the poors. Everyone else gets screwed and the problem of people needing cars doesn't change at all.