I've asked myself that question a thousand times and never come up with a satisfactory answer. It's one of the major weaknesses of III.
The best I can do (and it's pretty feeble) is that Michael saw Immobiliare as a way to launder the money he had left after selling the casinos, cashing out the other Dons and bribing the Vatican. Perhaps he thought he'd be subject to less scrutiny in Europe than in America, and the Vatican's imprimateur on Immobiliare would protect him.
I appreciate you trying, but even that really makes no sense (not meant to offend you, you didn't write the script). He's a billionaire. If he's totally out, as the film seems to imply, why even need to launder money? He cashes out the other Dons as we see even before he has control over Immobliare.
And subject to less scrutiny for WHAT, exactly?
Be protected against WHAT?
It's a shame that the central premise of the movie doesn't work because the movie around it (the Vatican/Mafia ties, Altobello, Lucchesi) are all interesting things. The weakest point of the film is actually Michael himself IMO both his central story and the way he is portrayed. We don't get to see WHY or how he changed back to being more like his pre 1945 self.
We're left with an embittered and alone Michael Corleone in 1968 at the end of II, and then in 1979 we have this talkative, nice guy who actually has a personality that is more a mix of Vito and an older Fredo than his old self. He's weak like Fredo (in that he is too foolish to see the threats around him and wishes to make peace with his enemies), overly ruled by his emotions like Sonny (IE letting his personal disdain for Zasa cloud his judgement) and timid like the older, sickly Vito was. It's almost like he had a stroke and his personality changed. Not even a semblance of the quiet, contemplative, almost genius level intelligence is there. Michael in II is like a master chessplayer whereas III he's like...A guy? Some weak mix of the worst of Vito, Sonny and Fredo? Too mired in the small details to see the big schemes around him?
