If I was building a company from scratch it would be a Linux shop. It would be hard to convert a Windows shop to Linux, but if starting from scratch you can design everything around it. Idealy, most programs would be web based. Stuff like ticketing systems, inventory, customer, that type of stuff, there's absolutely no reason why that stuff can't be web based and coded so that it works in any browser on any OS. Those type of apps are the core of most businesses, then anything more specialized could be figured out to be done in Linux. Possibly have some Windows TS servers or VMs for apps that absolutely need to run in windows and that there is no replacement for. Like Linux lacks proper CAD programs, so if the business needs that then they'd have a VM or TS server for that.
The idea would be that the workstations would not be specialized and rely on local programs. Then you can run pretty much any OS you want.
One thing Linux lacks though is any kind of central management. I'm sure it CAN be done, but it's FAR from turn key, like Windows/AD is. If Linux came up with a proper turn key AD like environment and better permission system (if you've worked IT you would know the native Linux permission system sucks and would not work in business), I bet it would gain a lot of traction in business use. I could see schools use it too. It needs to be turn key, though. nobody has time to read 100's of pages of documentations for something that is done in a few clicks in Windows.