That all sounds logical....but, put it this way....if in fact this is a new, devastating disease that's going to wipe out the spotted eel population, I know you understand the futility of removing even 100 or 1000 of them from the wild, if you can find them, and hoping that you've eliminated the problem. Leaving the eel or killing it won't affect the eel populations or health of, in the least. If that's a serious disease, they're in trouble, if not, he'll just go by the wayside and be a memory....the weird eel.
If this were an isolated herd of...buffalo, or goats on an island that you can see and monitor... maybe...but eels in the sea? good luck.
There appears to be just this one, at present. I prefer *preventative maintenance*.
I also don't like leaving crippled animals to fend for themselves over long periods of time. If I can't help it one way (treatment), might as well help it another (euthanize).