it's only a fundamental problem if you already decided that the obvious solution (policing the illegally parked cars) is impossible. New residents owning cars

it's only a fundamental problem if you already decided that the obvious solution (policing the illegally parked cars) is impossible. New residents owning cars which they cannot park on the street without being towed would not affect current permit holders at all. Sure, policing might not be done now. But is that because it's not worth doing/nobody cares enough, or because there is some law of physics which makes it impossible? Even a street sweep every few days immediately after most people arrive home from work would massively change the risks of parking illegally.