The DVLA website says that if a vehicle was last taxed before 31 January 1998, you do not need to make a SORN. I sent in a SORN form for an old bike, with a letter asking whether "do not need to" means "are not obliged to" or "are not allowed to". Six weeks later, I have had a letter in reply. It just states that "you do not need to make a SORN". Although it does not precisely respond to my question, it seems to imply that you cannot make a SORN even if you want to. So that's an answer, which is quite helpful in its way.
Until you tax it again then you're back on the whole SORN/tax/insurance nightmare/gravy train of maximising fines from forgetful people who make a genuine error and making it as difficult as possible to buy/sell a bike...