In the US the main function of the federal govt is to do those functions in which the individual States couldn't do as well. So, general or national defense fits this. As does controlling money supply [Federal Reserve]. And such things as international trade [foreign policy in general] and deciding matters regarding interstate trade and commerce.
Managing schools, managing "retirement plans", or welfare program of various stripes, or the numerous other kinds of pork is not the proper role for the Federal govt.
But because of various highly publicized cases of "massive" corruption at the State level and mainly because southern States were not adequately correcting the various injustices due to the slavery of blacks and the maintaining state law or "accepted" practice which discriminated against blacks, it was seen as necessary that the Federal govt to have more control over individual State's power.
Add in a few other things like the Great Depression and "The New Deal" [which didn't actually do anything effectively in terms of getting us out of the Great Depression, other perhaps make people "feel better about it- because "someone" was saying they were doing something to address the problem" [and considering federal management of the banking system was probably one of major causes that at least *added* to it's severity, it's a bit silly to assume the federal govt played an effective role and was the "hero" in resolving this terrible state of affairs. I.E the reason we have not had another "great depression" is because the Fed and central banks in general have a better grasp of what actions to take- not because of various social programs and higher taxes].