Oddly enough, I understand that certain kinds of pre 1960 commercial (in private use) are already MOT exempt. I think that one of the reasons for this proposal is to align other vehicles with those commercials. The overall logic is undoubtedly that most pre 60's cars are more or less collecters items, owned by enthusiasts, who look after them well and use them infrequently.
The MOT is a valuable annual reality check, but it is only a snapshot in time, far from a guarantee of roadworthiness, and probably takes relatively few cars of this sort of vintage off the road in real terms. Plus there are becoming fewer and fewer MOT testers who can give a realistic assessment of the condition of a fifty or sixty year old car and it will become unreasonably hard to achieve a sensible pass as years go by.
I think that, on balance, I would be more concerned if the exemption had been , say, pre 1970. There are after all, relatively few fifties and sixties cars that survive, even fewer that are likely to be used as daily drivers. There are hardly any 1940's survivors at all and then pre war, you are getting into a sector of the marketplace where cars are getting quite seriously valuable and are even less likely to be neglected or used on a daily basis.
There are risks. There will always be the odd idiot who will be tempted to drive his car when he knows that it is defective, but the percentage compared to those who already drive unroadworthy high mileage modern cars in an erratic fashion, is probably negligible.
I foresee that the police will become more interested in old cars on the road, and that if you attract the eye of the law with some ratty old unrestored barn find, you will be required to demonstrate that your car is roadworthy. Interestingly, the insurance market has been fairly quiet about all of this. I suspect that they won't hike the premiums that much, but will make it harder to claim, any classic involved in an major accident, being subject to engineer's scrutiny before there is any payout. Heaven help you if you have not kept it up to scratch. In short, owning a classic may become easier in some respects, in that you won't have the annual stress or cost of the MOT, but it may become riskier in terms of liability if things do come to grief.