Android is built on the Linux kernel so actually if you hook a keyboard, a mouse or such in the micro-USB slot on your phone it should just work out of the box. I don't think there's that much consumer interest for hooking up a 10x sized a keyboard to a smartphone though. It wouldn't be a big push for Google to bring out a dongle-sized concept PC based on Chromium OS or Android if such devices prove popular, however.
And if you are willing to hack some there's of course the business-card sized Raspberry PI that has decent ARM CPU, HDMI out and USB in that can be flashed with your favourite Linux distro, Android or Win 10.
Why bother trying to create an open home brew environment around a closed platform?
Cost and availability of hardware? While the original platform/OS might be closed, it might be possible to root it and get raw access to the underlying hardware. With original Xbox this was super easy, since it was essentially a cheap Intel PC in a console box. There was a very lively hobbyist culture around the original Xbox with many people installing Linux on it to convert it to an affordable HTPC.
Is this the first Linux product being offered by Microsoft?
Definitely not. This might have been so in the 1990s and early 2000s. But Microsoft is nowadays a major kernel contributor and has been offering Linux as a first-class operating systemn on the Azure cloud computing platform since at least 2010.
I haven't lost my mind -- it's backed up on tape somewhere.