Only if the city has the right to bar travelers from passing through.

A lot of road infrastructure funding at the town/city level can disproportionately go to wear/tear/usage by people/trucks that don't live in the town and the taxpayers don't benefit (in fact often the opposite). It makes more sense at the state level especially if you factor out interstates and in fact that tends to be how things are handled much of the time in the US.

Only if the cities are barred from encroaching upon or demanding access to bypass highways.

Yes, that’s fair, but we know the vast majority of trips are local outside of certain exceptions.