What makes you think that? Those inflexible workers are also those who make the purchasing decisions. A shop full of Windows admins will not switch to Linux unless forced to (and vice versa).
And many will eventually be outsourced. In fact, systems administration as a profession is on the downswing due to the cloud. This site itself is largely focused on "disrupting" inefficiency with automation.
Not only due to cloud; even if you have local bunch of immutable OS instances like CoreOS or RHEL atomic running containers, you don't need a big staff babysitting server OSes.
Most definitely not. There are a ton of Microsoft Certified Somethings that will refuse to administrate Linux servers unless their life depends on it.
Source: I work at SAP's internal cloud unit. We have to support Windows VMs (begrudgingly, if I may say), even for payloads that could run on Linux.