There's a difference between what an individual club needs and what a league needs.
For Milan or any individual club? Yes, winning is all that matters, but when it comes to raising the profile of a league, if one team wins over and over again, it stunts the growth of that league, and subsequently it stunts the growth of Bayern. PSG is state-backed, none of its revenues are organic, Ligue 1 could collapse and they'd be fine.
The Bundesliga should be a much bigger league than it is. It has great stadiums, amazing fans, top-tier production, lots of attack but there is little jeopardy. Everyone expects Bayern to win.
There's more to it than just competition though, I think you need stars to bring attention to your games, and the transfer fees is part-and-parcel to attracting eyeballs to your league.
But you also need rivalries. The NBA was on the downswing until Magic and Bird came into the NBA--the subtext (to put it lightly) of those rivalries mixed with the teams they played for led to a massive spike in interest in the NBA which Jordan came in and exploded even further.
Rivalries, though, is what fuels any sport. Women's basketball was supercharged with similar dynamics to the NBA with Magic and Bird, with Clark and Reese. Reese isn't at the same level as Clark, otherwise, they would have a massive hit, but they needed that.
I agree with you completely, the way to raise the profile of Milan is in the CL, that's why PSG is growing, more than having stars, or big transfer fees, or any of that. If Marseille, Lyon, and Lille started spending money like that, and winning in Europe? Ligue 1 would grow. Any league would.
Milan needs to win to expand the brand, but absent that, it needs to be in the CL at the very least, which Redbird have failed twice-in-a-row.