The inconsistency that people have noted in Emet's writing results from flanderization. His original story arc from late Stormblood through to the end of the 5.0 MSQ was enjoyable, and he was an interesting villain. He's ultimately an Ardyn expy, but a well executed one.

What him uniquely popular was Azem, and the last minute revelation that we were secretly friends all along from another life. Couple that with the transition from 'You will not inherit our legacy' to 'Fine, you can inherit our legacy' and you have a strong audience hook.

The end result of this popularity surge was that the Tales of the Shadows short stories and Endwalker flanderized him from ruthless psychopath to facepalming softy. It's a bit like trying to redeem Kefka or Sephiroth and turn them into your buddies at the end of their respective stories. It would make for a cute AU spin-off manga idea, but trying to actually work it into story canon makes for a bit of whiplash. I think that's what people take issue with in his writing.

It's perfectly fine for a villain to just be a villain.