Never under-estimate the ability of Microsoft to be massively incompetent.
The first and most important point I would bring up is that Microsoft cannot afford to alienate gamers, because it cannot afford to lose such a large share of a market that is already threatened.. Shamus mentions the idea that
The vast majority of PCs are sitting in office environments or are used at home for non-gaming things like web surfing and word processing.
But Windows' hold on devices for "non-gaming things like web surfing and word processing" is in serious danger. Tablets can do such tasks quite well, with the added benefits of faster accessibility, fewer updates, less physical space, and (often) lower prices. Chromebooks can bridge the gap for those who want more dedicated PC-like hardware, and as screen-broadcasting technology gets better and better, needing a device that doesn't have a small screen for ease of viewing or making presentations becomes less and less of an issue. Microsoft's share of the mobile market is utterly pathetic, and the murmurs of "Windows Desktop as a Service" have as much to do with businesses' fury at the haphazard and sometimes self-sabotaging way Windows 10 handles updates to the machines on which people are conducting work as anything. Microsoft's attempts to make their full-scale computers more tablet-like, like the Surface, have both plenty of competition and their own issues with reliability.
Anecdotally speaking, I already know people who used to use computers all the time and never turn them on, but are constantly buried in their phones or tablets. Also people in academia who curse the day they upgraded to Windows 10 and its bloated, bandwidth-hogging, "I'm taking over your computer in the middle of what you're trying to do" attitude.
And then there's Apple, which still has its own computer division, iPads aside. Apple is already beloved by many in arts and academia, many of the popular file formats are cross-compatible, and they aren't subject to nearly as many updates or viruses; how much of a push would it take for businesses to decide a sleek Macbook was their work computer of choice?
The bottom line is that Microsoft is on thin ice with a lot of people; even if Steam gamers only make up, say, 10% of their market, it's a large enough segment that they would be foolish to alienate. Especially as gamers have garnered a reputation for being famously irascible; if 10% of your market goes on to their schools and jobs and blows steam out their ears (no pun intended) on seeing the windows logo on their monitors, that could have a very real cascade effect. You don't start stomping when you're already on thin ice.
The second point I would make is that Microsoft's market and UWPs are terrible, as Shawn noted, but they're also terrible in all the ways that are so typical for Microsoft: The "make a product that's not as good, bundle it with the system, and hope that people saddled with it will play along" approach. Internet Explorer? Games For Windows? "Always On" Internet that locks your XBox One games to their system? The freaking power button and start menu in Windows 8?
Yes, Microsoft could make a games market that competes with Steam on both features and game availability. But it's far more likely that they'll do what they usually do: design from the top-down with the goal of exerting control and the idea that their people know what the end user should want better than the user does, discover exactly how mistaken they are, and backpedal with about as much speed and grace as a multi-billion dollar behemoth can.
Unless they essentially had a moonshot- a crack internal team with the wherewithal and freedom to design a Steam competitor without interference- Microsoft is unlikely to produce something that can compete with Steam head-to-head. And given what they actually seem willing to throw at the project, viz. the Windows Market, UWPs, and bundling- putting more resources into the same lousy tactics has to seem like throwing good money after bad. At least to the usually results-driven people who decide where to put the budget.
My third point is that Microsoft actually seems to be moving in the opposite direction- making their console games available to PCs rather than trying to push PC users onto consoles to do away with a "troublesome" market sector. Little wonder; the XBox One attracted a lot of ill-will on its release, and remains third in the wake of the Switch and Playstation 4 in recent sales, despite the push of the most powerful console on the market, the only truly 4K console, yatta yatta yatta... If nothing else, it speaks of a publisher that would rather see its games available on both XB1 and PC to maximize sales and take advantage of a uniquely poised ability to efficiently create multi-platform releases (and might even be under some pressure from third parties to make such a broad market available).
That Valve would like to move Steam away from Windows, I have no doubt. And there may well be people within Valve with similar thoughts as Shawn's. But I also have to seriously wonder if there aren't people who are less afraid of Microsoft's attempts to control the market than Microsoft's potential to bring down the whole ship before they can launch the lifeboats.