I'm not sure that logic plays through. Frankly, for Microsoft, the real problem is that damned few people really even consider Microsoft mobile products at all. They're a niche player, competing with BlackBerry for who will end up pushed right out of the market.
Imagine you're Microsoft, you're faced with the possibility that you will never, even if you heavily subsidized a mobile Windows product line, be able to make any significant headway into the iOS-Android hegemony. What would you do? If it was me, I'd quietly admit that I'm never going to be able to dominate mobile platforms the way I do desktops and portable computers, and I'd leverage what I had by opening up my software to more platforms.
This isn't even a revolutionary idea for Microsoft. They once owned their own *nix platform; Xenix. Windows NT itself was designed a hardware abstraction layer so it could be ported to multiple hardware platforms. But somewhere along the line Microsoft and the x86 computer manufacturers welded themselves together. I can't say it was a bad decision, as it made Microsoft and Intel absolute shitloads of money for a quarter century, but at the same time it seems to have frozen Microsoft in place. It became a one-trick pony, only able to envision itself in a world of Backoffice apps and OEM licensing. Now it's got to be nimble again, and as it has already effectively ceded a large portion of the computing products out there to Apple and Google, it's got to make the best it can with what it has.