Allardyce was the one that was totally unpopular from day 1. But I think they panicked giving the situation at the time. And I think they realised soon enough it was a mistake and acted on it. They aren't that out of touch with supporters especially with so much social media .I'm not sure anyone so far is overwhelmingly popular. I'm not sure Moshiri cares too much about what the fans think, though. He did hire Big Sam after all. Maybe he takes the Eddie Charlton approach to these things: "What will the fans think? [Poor language removed] the fans!"
I'd be very surprised if they appoint one of the first 4 I mentioned anyway. They know from day 1 it's going to bring too much tension from the supporters.