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.

A road in a random neighborhood is still important to me even if I can't cut through it: The mere fact that I can easily travel to any destination connected by it is very valuable, even if I don't frequently use that ability for any single specific road segment. In addition to my own use, its very useful to me that other people I interact with can reach those properties (so that they can live near by and engage in commerce and friendship with me).

A complete road network has greater value than the sum of its components in isolation, and this is true even for components even where you can't use them for non-destination travel.

Following your logic, any sub-graph of roads that can't be transited to other subgraphs should entirely be paid for by the connected properties-- and that clearly is not how we do things.

Moreover, the "if I can, I should" thinking strongly incentives making neighborhoods into single-access navigational cul-de-sacs, which creates worse traffic for everyone when the local traffic for the neighborhood gets funneled into a single choke point and causes congestion.

A month or two ago I saw an image on reddit from florida where someone showed that it was an 8-mile drive to their backdoor neighbor due to a lack of connectivity between neighborhoods. ... that's the kind of garbage roadway network design we'd get if we can only use raw connectivity control the load and character of use of roadways.