Let’s start with a simple general definition: ‘compulsory registration’ is what happens if the sender of a letter doesn’t register it, but the Post Office decides it must be registered anyway. Put like that, I suppose it sounds rather arbitrary – but where compulsory registration has been resorted to, it’s been for very practical reasons.
People who enclose coins in their letters have been a perennial bugbear for the Post Office. It didn’t take advanced deduction skills for a sorter to realise that the small hard round object they could feel inside a letter was probably a coin, and hence worth stealing if they were so inclined. A regrettable number of postal employees over the years proved to be so) was thus a natural expedient to reduce losses from the mails (and also to protect said employees from themselves).