I quite agree. I can spot an oil leak, tell if the car is running too rich from its performance, tell if the brakes work when I press the pedal. BUT, rust on the chassis, bits underneath coming loose etc. No, I need someone to put it on a lift and have a good look from time to time.
My classic here has to have the french equivalent every 5 years, I can take it for voluntary tests of course as well. A classic put on the road before 01/01/1960 is totally exempt though. Mind you that date is fixed. These rules do only apply to cars registered as 'Collection' which means pretty much standard in terms of engine.