I think you’re looking at things backwards.
These days, I doubt it is Xbox/Microsoft that doesn’t want their games on other systems. If anything, Xbox Game Studios would be happy to have their games on more systems. Microsoft realized that there’s no reason to keep “console exclusives” when you own Xbox, and essentially own PC (windows) and with cloud gaming, they can handle the software end.
I feel that the issue is more that Sony and Nintendo don’t want the Xbox brand on their systems at all. For example, Sega, a company with no hand in hardware anymore, sure, they can put their games on any system. But so long as Microsoft is working on Hardware, then I doubt it. They don’t want people who have a Playstation boot up a game and be greeted with the “Xbox Game Studios” message and think “Hey Xbox made this game, maybe I should buy an Xbox.” and then lose someone.
PC is the only place that is neutral ground, but even then Sony isn’t willing to release anything day-one on PC. One could say that they are trying to catch up (and at the rate Sony is putting stuff on PC, I would believe it) But none of the upcoming games are coming to PC on launch day. They want their games to be timed exclusive, so if you can’t wait for God of War Ragnarok or Spider-Man 2 (loving the Spidey PC port BTW) then they want you to go buy a PS5. As for third parties, chances are if you’re on PC at all, then that’s where you play your third-party games anyway. Before you just bought the other consoles just for the exclusives (if you’re one of those that have the money for a PC AND a console). Sony realized that PC is an untapped market for them. And porting is easier than ever since hardware wise consoles really are just micro-PC’s these days. You’ll always have the few that try to own every console, but most people have their one system and they’re done. Especially PC players. But if they can try and squeeze a playstation out of a PC gamer’s wallet, then they’ll try. Admittedly Minecraft is on Playstation, but they don’t advertise that they are an Xbox owned company right up front like they do with Gears, Halo, or Forza. Mojang is still Mojang. But Sony still doesn’t like playing with the others. Even for Crossplay. Even Fortnite which makes plenty of money as is, had to pay Sony for them to be allowed to use Crossplay. Most publishers still have to pay Sony for crossplay. Even free next-gen upgrades is too much intermingling for them. (Sorry if this sounds like I’m dissing Sony, but they are reluctant to change with the times.)
Nintendo is a similar boat. The Switch could easily work with MCC (except the file Size). Heck, Xcloud would be a benefit to the Switch too. But Nintendo doesn’t want the Xbox name on their console. What separated Nintendo from Sony is that Nintendo doesn’t really care about third parties (specifically Western third-parties) to begin with. Bethesda/Zenimax got a pass since their games aren’t outright popular military shooters. (The closest would be Doom or Wolfenstein, but they don’t fit the mold either, one being Demons, and the other alt-history rebellious run-and-gun) Nintendo tries not to cater toward the trendy-western thing. Except when it comes to history (or rather, having other studio’s history on their console) Banjo Kazooie was in Smash Bros and Xbox owns them. But Banjo Kazooie was famous on the Nintendo 64. I don’t think this was Nintendo doing Xbox a favor, I think this was Nintendo doing Rare a favor. Especially since there hasn’t been a Banjo Kazooie game in a long time and I doubt there ever will be one no matter how many Millennials/Early Gen-Z’s ask for it. Bringing up Zenimax/Bethesda again, many of their games have a strong historical presence. So does Minecraft, which I brought up before.
So again, I don’t think it is Xbox that doesn’t want their games to go to other systems. I think the other systems that don’t want Xbox “invading” their turf.