Anyone with a correct understanding of the problem domain would know you have to cope with missing plates by indicating they are missing and not by using (many) different sentinel values. The fact each city/county/state uses a different value indicates the whole ticket processing system is a screwed up mess.
The North American system of plates essentially identifying a person and not a vehicle is weird. The UK still allows vanity plates but they are bound to the vehicle (and to a current keeper - when you sell it the plates go with the vehicle to the new keeper unless you make special arrangements). I still find it odd to take the plates off a vehicle being sold and to have to get them put on to the new one.
A vehicle without plates in violation of traffic/parking laws should be towed (or in some places it could be blown up as a security threat - Northern Ireland that used to be a regular event and a joy-riders post-drive fun to remove the plates and wait for the fireworks).
At least if it is towed, the fines can be sorted out before the return of the vehicle rather than wasting time (and money) on a no-hope chase of some unidentifiable owner unless some schmuck happens to have a vanity plate matching your chosen sentinel value [in which case you then have the extra expense of wasting time cancelling the ticket or even wasting court time before it gets dismissed].