Streets have many purposes. They allow people to access their homes. They provide parking. They are bike routes, walking routes, scooter routes, running routes, skateboard routes, and driving routes. They are sometimes even places kids can play, or at least where parents can feel safe biking with their kids, or where one can easily and safely cross the street as a pedestrian.

Not letting vehicles cut through a neighborhood street means the street serves one fewer purpose, but it means it serves every other purpose much better than before. Maybe it's worth it for some streets, maybe it's not for others. But your statement is a bit like saying you shouldn't need to pay taxes to maintain a school because you're not allowed to drive through it.