The law usually when somebody does this changes to prevent others taking advantage of a situation
The law has to allow you to drive a car to and from an MOT, otherwise it would not be possible to tax cars with an expired MOT. If you could pay the tax without the MOT, this would all be moot, but you can't.
Then we get onto which garage you can use. Define "nearest" - nearest by time, nearest by distance. If you're going to define "nearest" then the legislation has to handle every eventuality so people know how to obey the law. What happens if the nearest garage is no longer the nearest because of roadworks? Again, the citizen has to know how to obey the law.
Same with time. Does the car have to be picked up immediately? What about a car dropped off for an MOT, and the garage closes before the owner has returned from work? At that point should they report to the nearest police station? What happens if the garage attempts to fix the car, but can't get the parts and asks the owner to take it away? Does that make the owner a criminal?
Far easier to say "you can drive it to an from an MOT garage". As long as they can demonstrate they were making that journey, that is fine - and it works perfectly well.
When I lived in London, I often drove to Maidenhead to get the car MOTd - because I trusted a specialist there to do a decent job - not to pass the car with defects, but to actually look at the car and tell me (MOT issue or not) what needed doing.