Due process? They don't need no stinkin' due process.
The owner of the vehicle would have to be demonstrably responsible for the vehicle’s illegal “status.” That this absurdity has passed muster for decades does not mean it’s right or even legally supportable.
The bottom line is that municipalities have to control parking, so they need a coercive tool to do it. They could tow the offending vehicles in every case, but that would be expensive and disruptive. So they’ve taken the easy — and legally ambiguous — way out.