I think people who are passionate about specializing mostly have to do so on their own. Nothing wrong with allowing opportunity to be your guide. I enjoy most anything so I tend to be like you CB and just go along for the ride. I'm a generalist and never specialized.
But if you are passionate about HyperV or SQL Server then there is a lot that you can do outside of work to make yourself specialized to a point where any shop looking to use you as a generalist or for a different specialty would not find you cost effective.