My experience in the US is that smog tests are the exception, rather than the rule, and I don't know of anywhere that has an annual mechanical inspection with teeth. (I imagine there's at least a few jurisdictions in the US that have the mechanical inspections - I just don't know where they are or how serious they are).
The counterpoint to your final observation, is that there is very little of the US where you can (today) live without a vehicle. There are plenty of people that fall into the category you describe - able to maintain their vehicle but can't be bothered, and without the annual inspection, there is no corresponding forcing function to get those vehicles off the road.
There are plenty more people that can't live without a vehicle, and they can't afford to maintain it to a high standard (or they trade off food, clothing, and / or shelter to maintain the vehicle).
As a point of comparison - the UK is ~65M population while the US is ~320M (
population of the uk - Bing). That's in an area of 241,000 sq km for the UK vs. 9,100,000 sq km for the US (
http://data.worldbank.org/indicator/AG.LND.TOTL.K2). So ~5x the population in 45x the area for the US - we aren't packed in as well, and that translates to a need for more driving.
I suspect that one benefit of annual inspections with teeth is you don't have "rolling coal" as a thing (
).