> Why would they have any interest in Linux on the desktop?
Short answer: Chrome OS (also Android).
Chrome OS is a Linux distribution being aggressively promoted by a large, well-funded competitor. It can already run Android apps (in release versions) and Linux applications (in beta). Ironically Visual Studio Code runs really well on Chrome OS, as do the Android versions of Word, Excel and Powerpoint -- full screen like a proper laptop application[1]
Microsoft's applications already run on Linux; it's really up to Microsoft to decide whose Linux distributions they get to run on.
It would probably make more sense for them to support Android/Linux applications on Windows rather than trying to make Windows applications work on Linux. Especially since they're continuing to work on slimming down Windows and getting to run efficiently on ARM, I don't see why they would invest any resources into Linux on the desktop.
Considering how good a job Microsoft has done of fragmenting the UI, breaking things with frequent updates, and generally turning Windows 10 into a Goldberg-esque nightmare, it looks like they're already practicing running their own Linux Desktop Distro.
Short answer: Chrome OS (also Android).
Chrome OS is a Linux distribution being aggressively promoted by a large, well-funded competitor. It can already run Android apps (in release versions) and Linux applications (in beta). Ironically Visual Studio Code runs really well on Chrome OS, as do the Android versions of Word, Excel and Powerpoint -- full screen like a proper laptop application[1]
Microsoft's applications already run on Linux; it's really up to Microsoft to decide whose Linux distributions they get to run on.
[1] https://imgur.com/a/rp0VFR4