Yes. I feel like if you base Avengers on pre-bendis standards, you can still use elements of Bendis's run in other franchises.
Why arbitrarily destroy the Avengers franchise just to attach it to the Marvel Knights characters? You could have Luke Cage, Iron Fist, Doctor Strange, etc fight together under so many other banners, and have them fight the Hood and his criminal syndicate without commandeering the Avengers franchise. It could be Marvel Knights, Heroes For Hire, Defenders.
The fact is, Marvel doesn't have the most marketable members of the New Avengers team. Without Spider-Man, Wolverine and the Thing, it's sort of a C-list street level franchise. And you don't replace the classics (Captain America, Thor, Iron Man, Hulk) with Luke Cage and co.