I know I have plenty of small problems with my Linux desktop, same as I have with my old Windows desktops, but I generally know how to fix/learn to fix those without going to a support line. That would be true even if you gave me a Windows computer.
Essentially, if you gave the people filing all the Windows support tickets a Linux machine instead, would that fix the problem? Or is it that those people are more likely to need support help AND also happen to prefer/need Windows.