Some (not all) US states do an annual safety and/or emissions inspection. I don’t know whether this typically includes an odometer check.
Many states don’t do any sort of annual check at all; just pay your annual registration fee (tax), receive this year’s sticker for your license plate, and you’re ready to drive for another 12 months.
A friend of mine bought a new used truck many years ago. he was really proud of it, set about using body putty to fill the bottom of doors so we could no longer see daylight through the rust. We went on a road trip, doing about 70 miles an hour. At a gas station in a village 90 miles later, we stopped for gas, I looked at the times, and calculated we had been doing 55mph; and checked the odometer and it also was off. Wrong size tires…
My dad and I were driving in his 68 Jaguar sedan and he pointed out the odometer was about to roll over to zero again. I asked whether that was 200,000 miles or 300,000 miles and he said “I don’t remember”. about 5 years later, the leaf spring broke (rusted through) and then he could no longer get it safetied in Ontario because the underbody was so badly rusted.
Ah, those old cars. Nowadays, the electronic will probably die before anything.
It’s not uncommon for a buyer to take a candidate car to a professional mechanical for an unbiased assessment of its condition. The last used car I bought was from my parents back in the mid-90s, so this wasn’t an issue back then - but the person who bought my wife’s used car several years ago did indeed ask for a mechanic’s inspection (we brought the car in, she paid the bill).
A few years ago I looked at a used car at a brand name dealer and checked the electronic odometer. It said 25,000. Duh! A few years later I did buy a used vehicle (different model/year than the earlier one) from that dealer. Its odometer had a non-even reading. (They got smart?) I haven’t yet looked up the previous local area owner whose finance co. bill was in the user’s manual kit, to see if the odometer reading that was on it when he traded it was close to the one when I bought it.