You're not wrong exactly, but I think you're perhaps assuming an unnecessarily absolutist approach. If there are legacy systems that need windows, keep windows for those legacy systems. What you're describing are exceptions, not the norm. The vast, vast majority of public service computers could just as easily be running Linux.
As for who the Federal government sues, that's why you go with an enterprise release like Red Had or Ubuntu. You find a company that you're happy to work with, you pay them maybe 25% of what you're paying MS right now, and in return you get a full support plan with clearly defined SLAs.
This isn't so much "Nothing's impossible" as it is "It's really not that hard." These are solved problems. Plenty of governments have already switched over to open source.