The issue with Kang, Immortus and Iron Lad is actually a good example of what I mean -- it was basically a cameo and a reminder that the history of the team had been pushed into the background for most of the run.
It would be completely possible to write an Avengers comic with an all-new cast that felt like a "real" Avengers book if it played on the tropes of the comic and the history of the team. (When Ewing did Mighty Avengers, though of course it wasn't an all-new cast, people commented on how it felt more like an Avengers comic than the main one, just because of the stories he chose to tell.)
It's OK to dismiss this as nostalgia or nitpicking, but I didn't get the impression Hickman thought of the Avengers as anything more than a generic superteam with Captain America and Iron Man in it. Which is fine -- we've already seen this approach successfully taken in Avengers: Infinity War, where the Avengers didn't even exist as a team. But I think the Avengers are as much their own team, with their own history and specific tropes, as the X-Men, and I felt like Hickman wasn't doing what Bendis did and consciously challenging the way the Avengers used to do things; he just, in my opinion, didn't want to write about the team as if it had a history at all.