In my opinion this is the best option.
I already got windows installed on steam deck, but it would be a no brainer to have an Xbox OS, which allows you to play games from the Xbox app (GamePass titles) and do remote play/cloud streaming.
Who is with me ?
This Xbox OS would be installable on any PC, laptops, steam decks, other handheld PCs, full desktops etc.
It’s an interesting idea, I do wonder how people will use it to try and crack Xbox os though. Would just being able to emulate like we can currently be enough? or would people want to get more from it like on PC?
There’s also the fact that the games would all be optimized for Xbox hardware, and without anyway to change the settings (I don’t think that devs will take a PC type of experience where they give us full control of everything) . Whatever hardware we use will likely need to out perform Series S at least.
I have always thought they should release an Xbox OS myself. I envisioned it being what steam machines were meant to be, but actually be able to play all Windows/Xbox based games. Just build whatever spec’d PC or device you can afford or want and turn it into an Xbox. There would be compatibility issues with different hardware, but I am sure Microsoft can make it work.
I like this idea. More options.
Negative here would be a Microsoft handheld would be partially subsidized (like a Steam Deck) and be priced well whereas a third party one is going to just be pure profit.
Would be nice to have a Xbox layer on top of windows for the existing devices though.
Xbox games doesn’t come with setting options. The only flaw in this very neat idea
Will have no issues for devices powerful then series S
But below that, experience won’t be good
What they should do is launch a Gamepass OS running on windows and have xbox compatibility layer
With windows, any PC game will be payable and it will solve the issue for recent and new games
Having xbox compatibility layer would make BC and old xbox one games play as native on most devices today as they are more powerfull then xbox one these days
Make the OS part of Gamepass Ultimate service as well
If MS puts out an Xbox OS it would be a lightweight windows.
I play pc GamePass titles on my steam deck via windows fine. You can toggle system settings of PC GamePass games as they are PC games, and make them run how you like on your device
Whilst this is a great idea it is almost impossible, and negated entirely by Microsoft’s own strategy that we are seeing play out right now.
Xbox OS: I imagine the idea behind this is a way for games to play locally rather than via the cloud. This is a fair and understandable concept, and one that makes sense, but the OS is not the only thing that makes a game run. The OS could run like the Steam Deck’s Proton layer, where it emulates the Windows libraries to allow for games to run “on Windows” on the Steam Deck’s OS, but it is only because the Steam Deck platform has a base layer of hardware that this makes sense. Scaling Xbox games (and even Xbox PC games) to run across these different platforms would be hugely difficult at best and almost impossible at worst.
Hardware: Your phone isn’t built to run games like the Series S or X, and that’s evidenced by the drop off in power between the Series S and the Steam Deck. Building a gaming device needs power or comprimises, and without knowing exeactly how a hardware layer runs, you cannot be sure the OS will be able to be running on it. Hardware is a huge barrier here, sadly.
What even is the Xbox OS, anyway?: This one is intersting and might need more thought; how exactly would you get the OS on your device? In the case of Steam Deck, flashing it to run Windows is do able becuase it’s a laptop essentially, but Xbox OS would need a way in - and a universal way in, to boot. Not impossible, maybe, but not many folk would be interested in flashing their Android tablets to basically become Windows Phone devices 
What is the benefit?: What you’re describing is essentially a more complicated, harder to market, harder to build, and harder to manage version of Xbox Game Streaming. By keeping all the processing server side, they control the hardware layer and do not need to even worry about the client side hardware. I get that it is not local (and I have dreamed of a way to have “local streaming”, and your suggestion would be it) but there is very little benefit to their approach that they are taking now.
With a HUGE caveat.
There could be a way to make an Xbox style hardware layer, like Steam Machines, that devices CAN meet. I mean streaming does all the hard work, but if MS wanted to make a Xbox Surface device, then that would pave the way for investment in the OS that you’re talking about.
Sorry for the rant