I don’t particularly like or use them, but many times I have seen beginner to medium experienced kayakers drop their paddles upon exiting.
If at sea and alone, in those typical situations, a leash would be a backup and keep other options open. And there’s nothing like backups and options.
There are other situations like being in a narrow kayak while drinking/eating/photographing/dayhatching/bailing that a leash might be a temporary solution for paddle control. And of course, paddlers with ability/handicap issues might be well served by various types of leash solutions for the particular issue. On this particular instance, I could well see the utility of a pfd belt leash for an on water arm injury.
And in re-reading the above, I guess these situation would have to include a greenland paddle as well – although it does seem to be a stretch in some circumstances . . . but if the option was paddle loss? For a beginner, alone and in conditions?