I think MS will use their newly purchased assets in a way that will make them the most money. Since they would make money off any Skyrim or Fallout or DOOM purchased by someone for PS5 or Switch, there is no reason for them not to pursue that market. They don't just make money when they sell an Xbox copy, this is something a lot of people are overlooking.
These are franchises famous for selling across all platforms in multiple releases and re-releases, making millions and millions of dollars. I fail to see why MS would stop that money train in order to be exclusive. They can simply flood the market with IP they own and reap the rewards. Even if someone buys Skyrim 2 for PS5.
This is why Playstation is expanding to PC with some of it's releases; if you go cross-platform, you can sell more games. It's smart business sense. Expand your market.