Here it's not that uncommon actually. But here it's the Public Roads Administration (vegvesenet) that comes and takes your plates, and not the police. And I suppose they might have more time on their hands than the regular police. But it sounds like the process is the same here if you get caught driving without everything being OK. A while ago a friend bought a car and it turned out the previous owner had gotten stopped due to excessive noise and broken taillight, and was not allowed to drive the car until he repaired it and showed it at the inspection office. Instead of doing that he sold the car without telling about the problems. My friend drove around with it for about a week until he received a letter that stated his car was not allowed to use, and he had 3 days to hand in the plates before they would come to his house to remove the plates. And there's no way of knowing without being the owner if the car has been declared illegal, so my friend was clueless about it until he called the Public Roads Administration to ask what the hell was going on. He was lucky he was not stopped while driving or else he would have risked both fines and lose of license unless he could prove that he bought the car without knowing it was illegal.
Another story, last autumn I was out working on my car when one of my neighbours approached me and told me that he had parked his mk1 Forester outside his house and when he came back 15 minutes later the plates were gone and asked me if I had seen who had taken them. I had not seen who took them, but considering the car stood the entire winter without any plates and with the bonnet improperly closed I would assume a car from the Public Roads Administration had spotted him driving either with an expired inspection or insurance and decided to follow him. If it was a common thief that stole the plates for whatever reason, you'd think he would get some new plates within a few days.
I have no idea how many ''illegal'' plates I've caught, the site I usually check for car details before uploading doesn't show if it has valid inspection, but if I checked it for all my uploads I'm sure I'd get at least a few dozen. I've known it's a ''thing'', but it seems like it indeed is much more common than I thought. I've seen some incredibly bad cars on the roads over the years and it wouldn't surprise me if many did not have a valid inspection. I can't say that I respect people that keep on driving cars even after they fail inspection.
Here's an interesting one, also from my neigbourhood in Februrary.
https://imgur.com/a/yVSKNpW Temporary one-day plate was issued for 30th November 2019. But if you look at the small text that says the actual plate of the car is ZE 56119, and it has not been inspected since 2009! Yet every time I walked past this car it was cleared of snow and was parked in a new spot. However I have never actually seen it driving around, so there's a possibility that the owner just likes to start the engine and keep the car clear for snow. But then again, why would anyone do that to a rusty 27 year old piece of shit Nissan Sunny that hasn't been road legal for 9 years?