Except in this case we can't be certain that there even will be a fourth Xbox console. While the XBO isn't doing poorly, it's obvious that it's nowhere close to what MS wanted it to do. There's been enough reports in the gaming news media to think that there's a non-trivial chance of the XBO being their last system. MS has been really wishy-washy on the subject. While they've probably already made up their minds about what they plan on doing next generation, and I think the XBO still does decent enough in its best markets (mainly the U.S. & UK) to where the Xbox brand in general could and probably still does have a viable future, but I really wouldn't be surprised if next generation ends up just being Sony vs. Nintendo and we end up seeing Halo, et al., becoming multiplatform games.

MS most definitely doesn't need Xbox, at least as a hardware platform, unlike Sony and especially Nintendo who are dependent on their gaming divisions. Xbox is probably the most expendable of the big three console brands, both to its parent company and to the console market in general (aside from the exclusives the XBO doesn't have much to offer that the PS4 doesn't). In fact, it'd probably be more profitable to MS in the long run to go third-party, release Halo, Gears, Forza, etc., for the PS5 and whatever Nintendo's follow-up to the NX is (I think the NX will itself be short-lived, a consequence of a mid-gen launch), and make quality Xbox-style controllers and other accessories for every platform (because controllers are apparently very profitable). Since Halo is the only thing that kept me invested in Xbox this generation, MS Studios going third-party would save me a ton of money, so in a way I do kinda-sorta would want them to go third-party.

I do have one reservation about them going third-party, though: reduced competition in the console market. Nintendo has always been a wild card, and unless they switch back to making conventional hardware to rival PlayStation, then Sony would have a de facto monopoly on the AAA sector, and if less scrupulous people become the decision makers in the future then they could end up trying to do what MS tried to do with the XBO. So, if Xbox does serve a purpose in the console market, it could be simply to keep Sony on their toes. I mean, Sony did have to adapt last generation after they lost a ton of market share to the 360.

I like the name "Xbox infinite". Reminds me of the Nintendo Revolution.