Yes and no. There are support characters that have carried over in the Bond films, and there has been some continuity - concepts and villains reimagined (such as Bloefeld and SPECTRE most recently). Even Judy Dench as M carried over from Brosnan to Craig reboots. So a new Iron Man film would be more like a Bond film, but yes it's true that the Avengers is an ensemble cast - so you'd definitely want to introduce a new Iron Man in his own flick to get the intro out of the way than introduce a new actor in an Avengers movie... though it's possible it could work; look at Bruce Banner and how that all worked out.
I agree that Iron Man doesn't have to be in a new Avengers film after RDJ leaves, but a lot of it really depends on who will still be around after the next 2 Avengers films; you don't want to just take characters and actors away and replace them with new actors playing old characters - unless you are going to do an ensemble "reboot" (for lack of a better term, even though it wouldn't really be a reboot - but that's what it would feel like if they replace all the actors at once). Maybe instead, introduce a new Avengers Team because maybe Thanos has devastated most of the originals.
Personally I like the gutsy choice, get rid of most of the old team, keep one or two as carry overs to a completely new Avengers team - give some new guys a chance. Use Scarlet Witch, Ant-Man, Dr. Strange and Black Panther as the "heart" of the new team and add all new characters - maybe Falcon can help them transition or be part of that team. Dump the rest. I would miss the rest, but you know the saying - no guts no glory. Create an all new team to keep it fresh - don't give it a chance to get stale.