When I was working at EFF I would complain about people creating "persistent unique identifiers", and particularly ones that someone can passively log. Many governments probably have classified databases that are more intrusive than the ALPR databases, based on electronic surveillance means, which engineers might have been able to mitigate through more cautious protocol design.
I've thought that license plates themselves are such a persistent unique identifier, but one that we sort of didn't notice until the recognition and storage technologies got cheaper.
The original motivation for license plates seems to be about enforcing safety inspections of cars (maybe also liability insurance?). Nowadays we also have a lot of other uses that have piled up. The top two I think are very popular: allowing victims of crimes involving motor vehicles to identify the vehicles reliably, and allowing police to catch fugitives in vehicular pursuits. Maybe these were actually even considered part of the original motivation for license plate requirements. Below that, still fairly popular, you have allowing non-moving violation citations such as parking tickets; allowing police to randomly notice wanted persons' vehicles that happen to be nearby; and allowing government agencies another enforcement lever for other stuff by threatening to cancel previously-issued plates. (Oh yeah, and nowadays also paying for parking online!)
I could imagine more modern approaches that would put more technological limitations on some of these things, but I guess any change would be controversial not least because you're intentionally taking some data away from law enforcement (which I think is a normal thing to want to do). The one that's really hard is the "victims of crimes easily identifying vehicles". If you replace license plates with something that's not easily to memorize or write down, the reporting gets a lot harder.
Maybe we could try to have license plates change frequently using something like format-preserving encryption (https://en.wikipedia.org/wiki/Format-preserving_encryption) so they still appear like existing license plate formats, and then prevent law enforcement agents or agencies from directly receiving the decryption keys, so they have to actively interact with the plate issuer in order to answer specific investigative questions about specific vehicles. If police receive a report of a crime they can ask to find out what the involved vehicle's displayed plate will change to on specific dates.
This would have the problem that a partial or mistranscribed or misremembered plate would be pretty useless (you couldn't easily search for, or detect, a partial plate match). You could add some error correcting codes to the plate numbers, but I don't think existing plate numbers are long enough for that. Also, if the plate numbers didn't change very frequently, you could probably partially deanonymize ALPR datasets based on recurring patterns of locations over time.
The best lesson is probably that, if you make a new technical system, you should be very cautious about the identifiers that go into that system, as they may still exist decades later, and used for new kinds of tracking and new kinds of surveillance that you didn't anticipate.