You know what?

Sure.  This is fine.

Obviously they've just created a situation where every case is going to require the cops to actually prove/attest in court that the vehicle with the tag on it is actually the one they were pursuing (they have essentially just used technology to create a minor chain-of-custody issue for themselves), but that just means the inevitable abuse is going to cause prosecutions to fail and the cops doing it properly will have to do ten more seconds of paperwork ctrl+c'ing an image from a dashboard cam into their report with the license plate.

Meanwhile, they don't chase people around and create entirely new dangerous situations for both the person they're chasing and random unrelated people.  Win/win.

I'm not the biggest fan of the cops but this seems like a fairly legitimate method to let them accomplish something that it is actually appropriate for them to be doing in a manner that's significantly less pants-on-head than their default idiocy.  Go for it.