This varies widely from state to state. In TX, this is one of the ways they make up for not having state income tax. A couple decades ago, FL basically charged a ($300?) fee for registering cars from out of state. AZ used to (may still) charge an ownership tax based on the 'original value' of the car, depreciated on a 17 year straight line. When I moved to AZ, it cost more to register my 10 year old car than it did to register it new in CO. I'm not sure how they determined 'original value', as it wasn't what I paid for it and I was never asked for any documentation.
Some states offer a bounty for reporting out of state plates on residents' cars. Not sure if TX is one of those.
When I was working in FL for a year, I had my CO plates ripped off. It was kind of a pain to get replacement plates as CO didn't want to mail them to an out of state address.
For a few years, my parents had TX plates on one vehicle, CO plates on another, OR plates on their RV, and AZ drivers licenses. I'm sure that would have caused an interesting conversation had they ever been pulled over for some traffic violation.