I'd allow law enforcement, with the strict rule that the scanner system would have to immediately throw away any plate that they hadn't received a warrant to se

I'd allow law enforcement, with the strict rule that the scanner system would have to immediately throw away any plate that they hadn't received a warrant to search for. So they could have the scanner operating at all times, but they'd never get a notification until they happen across one of the (very few) cars they're specifically allowed to track.