Why would Microsoft pay them to do that?
Multiple reasons, actually. MS, despite all claims to the contrary, still operates on Embrace, Extend, Extinguish when it comes to competing technologies or external systems they have to use. It has embraced the Linux ecosystem, with the subsystem for linux and azure amongst other things, but its (and the wider allied industry's) attempts to control the kernel development process hit something of a wall even after Linus was struggle-sessioned into accepting a CoC and Rust. The person in the video objecting to the Rust developer's attitude was Ted Ts'o, who was the target of a definitely-not-coordinated attempt at removal from the Linux development team after rejecting changes by both Microsoft and Intel to the kernel driver interface. He's a powerful voice amongst linux kernel devs and has been amongst the most vocally resistant to the sort of entryism that MS normally uses to gain control of competitor technologies. They can't get around him, so their attempts to extend mainline Linux with interfaces that are only useful to Microsoft and Intel are stuck,
Having a drop-in replacement for the Linux kernel, using a language with no standardised specification, would give Microsoft a golden opportunity to, if not absolutely control the broader linux ecosystem, at least divide it into industry-blessed and non-blessed parallel ecosystems. Lack of language specification means it can invent whole-cloth proprietary extensions to the language that force compatibility. The fact that the entire kernel development would be under the thumb of the sort of people who blindly suck corporate wang, as long as it has a rainbow flag painted on it, would give them the ability to dictate changes as they saw fit. They could even have an open and enclosed version of the kernel, with the enclosed version working on Azure and favoured for Subsystem for Linux, while the open version works as a way to draw people in.
Would it work? 20 years ago, it could have. It's unpredictable now, but that's never stopped MS trying before.