My 2 cents worth. 500 is not really long enough for smaller birds in many circumstances. My former 300 2.8 2 was super sharp and I miss it a little but it seldom got used at 300. At 420 it has hardly any more useful except perhaps BIF, so the 1.4X was seldom used. 2X lived on the lens and the results overall were very decent but 600 was not really enough in many cases.
Having moved to 400 DO 2, the 1.4X becomes much more useful and is an option for BIF. Still, 2X lives on my lens and other than the F8, that pairing is great in most birding circumstances.
If 500 wasn't bigger and heavier I think that would be even better but I'm confident that 1.4X and 2X would be on the lens a lot because IMHO 500 is not enough. There is an advantage now since sensor resolutions allow more cropping but locking on a birds eye when the subject is too small in the frame, or even finding it, can be challenging. Of course there is also the challenge of finding subjects when the FOV is too narrow but this gets rectified to some extent by practice.
For me a super heavy lens is out of the question since it eliminates too many opportunities and turns into a burden hiking. I'm sure there are circumstances where a long lens/fixed tripod setup is fine but it's not for me since I prefer mobility.
Jack