I've always seen "states' rights" as a dog-whistle of support for conservative positions on social issues (guns, gays, abortion, and friends.) In the absence of a federal law restricting gun ownership, states decide how to regulate guns. Ditto on gay marriage and abortion. It was also used as a codeword for support of segregation by Dixiecrats in the late 1940s.

I can also see the argument that states would be more efficient at handling certain governmental functions, and in those cases, your argument that consolidating things at the federal level would save money may not hold water. Obviously the feds should have a role in policing illegal immigration, but states are probably in a better position to handle the issuing of drivers' licenses, naming of state highways, etc.

Really, the term has so many meanings that it's virtually meaningless without some kind of description of what "rights" are involved.