turkeys are able to be farmed commercially in huge numbers. Eels cannot. They breed just once in their life and die after spawning. The rate of maturity is slow (in NZ long-finned eels some females don't breed until they are over a century old!). Every single eel caught and killed is an eel that has never bred. Because of their life-cycle they can't really be bred artificially (it has been done experimentally, in NZ and probably elsewhere, but it can't be done on the scale that would be needed to be commercial in any way), and they are caught in their largest numbers during the breeding migrations (when the eels are heading downstream en masse to the ocean). In Europe and Japan the native eels have been almost wiped out through over-fishing (and to a lesser degree other causes like pollution etc). One of the statistics I read a little while ago was that the numbers of glass eels returning from the ocean to Europe is only 1% of what it used to be. Most of the eel seen for sale in Europe and Japan is, apparently, NZ eel which is exported by the tonne. NZ eels aren't endangered yet but they are getting very close. As I understand it American eels are likewise very much on the chopping block.
So, all in all, I say no to Thanksgiving eel.