I think City haven't got that big name manager that players want to play for. Mancini is a bit of a tool IMO. Ancelloti is awesome. I think they need someone like Acelloti/Mourinho/Guardiola to entice the players they are after. They can easily outbid Utd, yet RVP came to Utd and if they fail to land Falcao this summer they are going to struggle again. Last years signings have all been a big disappointment except for Nastasic who seems to have a lot of potential.
SAF himself said Chelsea will immediately be a title threat again if Mourinho goes back, so I think there's probably something in what you said.
I don't think Mancini will be there much longer honestly