If driving into Manhattan were not an option, I would expect demand for housing in Manhattan would go up[0]. Of course, housing in Manhattan is already incredibly expensive...

I'm sure Manhattan would become very pleasant for those who could still afford to live there.

[0] (Suppose for the sake of argument my preference for commuting was driving,walking,transit (in that order.) With the option of driving eliminated my second preference would be to walk, which means finding housing closer to my workplace in Manhattan.)