This is definitely an element or a factor, but I think it's actually not true.
People generally buy PlayStation because of an ecosystem: The controller, PSN, their game library.
There isn't much Microsoft can do at this point to turn the tide on that.
- Would be difficult to replicate the PS controller without alienating core Xbox fans.
- You can't replicate PSN: Trophies, game saves, friends lists
- You can't import a game library
Even the part you mentioned about exclusives is difficult to impossible to replicate. Sony has spent decades building its 1st party studios, to the point where they've attempted the ability for these studios to be able to work on more than one project at a time and even that has seen struggles.
Microsoft can't put nearly as much into studios and projects because the returns aren't there and GamePass destroys that calculus as well. This is something Jim Ryan warned about but was largely mocked about.
If Microsoft were to put 200 million into a game, there is almost no way they get a return out of that game with the game being on GamePass. Especially if it is a single-player non-GaaS game. So that boat has sailed. This is particularly troublesome for original IP.
In the last generation Sony came out with Ghost of Tsushima, Bloodborne, Day's Gone, and you can even give them the nod for Detroit Become Human. Add Spider-Man to that list and it just gets a bit ridiculous.
Microsoft hasn't had a single success in this arena at even the level of Bloodborne or Detroit Become Human. They also rebooted God of War. Even if Microsoft partnered with Quantic Dream, their games wouldn't sell nearly as well without the backing of Sony.
Microsoft generally hasn't come out with a worthwhile single player franchise since Gears of War on the 360 and that was made by Epic. The franchise launched in 2006... That's nearly 20 years without a flagship IP.
DF continues to push the console war and reject the notion that it is over. You can see how sad puppy John Linneman is here. GamePass and PC GamePass destroyed Xbox.