Been on the job since '82, and YMMV depending on location, but I don’t know what “putting a warrant on a license plate” is. Never heard of such a thing. A county or statewide BOLO alert might be issued but not an actual warrant.
Around here the plate would be run and officers would have a conversation with the vehicle owner in the course of the investigation. Depending on the extent of the damage it could be a misdemeanor or a felony crime.
Depends on which city you live in. In San Jose the police can not be bothered with such things. No police report, no crime there fore we are in a safe city.
Just try to find the identify of the person and go on Judge Judy to get some money. You won’t gain anything by having them arrested, which seems unlikely to happen if the police didn’t seem them in the act.
Something similar happened to me. Someone had thought I had hit the car next to mine, while pulling out of a parking space. He got my plate #, and a while after I got home, a cop showed up at my door, accusing me of being a hit-and-run.
It’s been known to happen, but I don’t know about “all the time.” It’s extremely hard to make a case to a jury on a single person’s testimony alone. Usually there is also at least some other evidence - perhaps only circumstantial - to accompany it.