Many, many criminals are caught because they use their own car on the job.
That’s not just a “license plate number.” Think of it as a police identification number. This is a part of the war on anonymity. Most modes of transportation today, from cars to airplanes to boats require identification. It’s not for you; it’s for the police to ID you easier.
Same problem with rental cars. All it takes is a license plate number, which leads to the store, which will then reveal who borrowed the vehicle.
Even stealing a car creates problems. You’ve got to touch it and sit inside. You may leave fingerprints, hair, fibers from your clothes, or DNA when you sweat. If the case is big enough, investigators will check those things.
The American police state punishes those who make mistakes. Getting caught is easy; especially in cities with many CCTVs and licence plate readers on the stoplights.
The goal here is not to scare people too much. We want to impart how much attention to detail is necessary today to get away with it.
What happened here was that the local news threw out a crime stoppers request. The public called in with information about a similar car with damage on the front passenger side. That was that.