I agree that big western style games are what might move more consoles. But it's more that if you don't have as much or more exclusives that are as good or better than the competition, you having a gap in you library like this puts you at a disadvantage.
It's not how good they do when they are there, it's how they hurt the platform's portfolio because of their abscense
What does Microsoft do well? Racing (Forza Horizon, Forza Motorsport), platformers (Ori, Cuphead), shooters (Gears of War, Halo). The only console that does better platformers is Nintendo, but that is not a negative on just how good Ori and Cuphead are.
What they have done is to ensure that they have acquired their second party partners and this will give them an opportunity to grow and hopefully better support will give rise to better games. Compulsion, Obsidian, InXile, Ninja Theory, The Initiative, Playground Games second studio are all working on story driven games. The type of games that Microsoft has been lacking in quality most of this generation.
If Rare can go back to the form that they had when they were releasing Kameo and Viva Pinata, then Microsoft will be in a good place. All they have to do is to try and get Japanese titles onto the platform and maybe invest in one or two of their own. The widespread investment that type of game will not move consoles for them, and I would wager that if they are doing better than they are this generation and that the gap in sales is not as huge as it is, then you will see these developers putting games on the Xbox anyway. If they cannot be moved to do that, then it is their loss.
I am also against Microsoft paying them to port games to the platform.