There is no real business case.
why not? If it's cheaper and compatible, why not?
Besides businesses have an all in one contract with Microsoft for Windows, Active Directory, probably SQL Server, Office, a certain number of seats for MSDN for their developers, Azure DevOps (separate from Azure - it’s the modern equivalent of Team Foundation Server), and the list goes on. They don’t care about saving a couple of dollars on Windows license.
Sure, but how much are they realistically going to pay for it?
I guess improving compatibility with general-purpose Windows apps might help them sell a few more Steam Machines, but it's hard to think that it's really going to move the needle.
Nothing? Valve makes it money selling the games on the store. SteamOS is presumably free to install on your own hardware once it has a general release.
Right, so my question is how does better compatibility with (non-game) Windows apps help them make more money?
Valve wants independence from Microsoft Windows, a better Linux desktop is part of that.