In a nutshell -- because it's illegal; because we'd have anarchy if everyone ignored the law. ... and the law doesn't have to (and often doesn't) make sense.Nothing I have read here answers my original query. Arguments about what is or is not a law do not answer the question. Why may we not spend a night in our motorhomes elsewhere other than our drives. We do not need to get out so we are in our own environment safe from disease transmission in either direction. Yes 2cv as you say "due to accident, breakdown or illness" sounds like a fair point but this applies just as much to those travelling anywhere, allowed or otherwise for reasons legit or otherwise so why are we not allowed to stop overnight? It makes no sense.
You asked "What possible problem might an overnight stop cause because of Covid19". If just one person did it, quietly and with nobody noticing, there probably wouldn't be an issue. If hundreds did it and ended up parking so close they couldn't open their habitation doors, provided nobody breached the containment a motorhome offers, there would be little chance of spreading infection. However, as previous posters have mentioned, there could be problems if lots of people broke the law in this manner. It would at least encourage others, including those not in the moho community, to break the law, which might well lead to a form of dystopia that you probably wouldn't find agreeable. Take a look at @Allen's post to see what's happening as people are extracting the urine out of the current relaxation of lockdown and ask yourself how these same morons would act if they perceived that nobody was taking a blind bit of notice of the rules.
Pragmatically, all campsites, pubs and other businesses that allow camping are closed. The Caravan Sites Control and Develpment Act 1960 makes it unlawful (with some exceptions) to permit camping in any form of caravan (including mohos) other than on licenced sites. So, you have nowhere in England to lawfully camp anyway. If, despite this, you choose to go wild camping, you risk repercussions from anyone whose dander your actions might raise and who might well go out of their way to put a stop to wild camping in their locality long after the current crisis is over.