The MoT test exemption for classics is the worst idea ever based on idiotic logic.
As you both have eluded to it always pays to have an indepndant check every year even if it's not legally neccessary
I know of a guy that runs around in a Triumph Herald that is akin to the Flintsones mobile, and what is still there is held together by pop rivetts and gaffer tape! Merely saying it's up to the owner to ensure roadworthiness is such a grey area as to be pointless, the owner could easily argue that it has been roadworthy as he's been using it for years!
As a former tester I have often had this conversation with the DVSA representative and whilst I can see that modern garages with younger testers may not be familiar with the curiosities of our older classics there was no need to completley abandon the process.
My own view is that it should have been downgraded to a seperate class of MoT in line with the classic status of the 40 year and older free road tax.
So you would then need a "classic" Mot test rather than a full regular test. In fact it would have been easier to say anything pre 1995 would be called a classic as then it would predate the cat test and make things much simpler with regards to emissions testing, anything before say Jan 1st 1995 would be considered a classic and exempt from that part. Likewise cars before then were unlikely to have items such as ABS and airbags etc so less electrical items to check, EML for example wasn't really a mainstream thing back then although there were a few creeping in from the likes of Volvo.
The test would be a simple affair, brakes checked with a decelerometer rather than in rollers, checks for the lights and tyres, make sure the suspension is in decent enough order, a corrosion check and that would about do it.
Crucially garages could opt out if their staff felt they were confused with classics, like the amount of free play in suspension on older cars that they are not used to seeing (an argument put to me for not doing a test!) so only testing stations faimilar and sympathetic with our cars would do them, which after all is where we go anyway. It would be simpler and therefore could be charged less, say a RRP of £30 which is enough for garages to want to do them for the half hour it would take rather than allowing nearer an hour, plus what garage that likes dealing with classics wouldn't want to offer the service as undoubtedly it would lead to further work once a customer becomes happy that they've found a place that treats them and their pride and joy with respect.
And as the guys have already said, the peace of mind that someone else has cast an eye over the car is well worth it. Wouldn't we all rather know of an impending failure?
Never has made sense to me, apart from the cynical view that it was done to get us older car drivers off the road if there became a spate of serious injuries with unsafe cars. But therein lies the answer I guess, the fact that there hasn't been a spate of crashes means maybe the system is working and most people get the cars checked anyway....