1) I believe urban areas--say, within half a mile of a subway stop--should be generally car-restricted to its residents, yes. (Exceptions of course exist but they can be managed; Boston has an MBTA car service for the disabled, as an example.) But no, cars don't belong where humans live.

2) As the sibling comments note, cars tend to park in observance of the law and don't go whizzing down the sidewalk while I am walking to work.