Moving the costs
Like it or not, the pool of Linux savvy tech staff is smaller than the Windows pool. So, if you move everything away from Windows, you will end up with a few new costs:
1. Retraining for existing staff
2. Increased costs hiring new staff with the skills needed
3. Reduced availability of specialists for the big/complex issues, and therefore increased consultancy costs
So, yes, reducing dependence on Windows is a good thing, but it shouldn't be seen as just a way to cut costs.
Investing in their staff is always a good thing though too!