Of course the majority will exercise their power at every opportunity. Jim Crowe was majority rule.
And yet it only persisted in one, less densely populated area of the country. The northern states didn't need federal judges to tell them not to enact such laws, because the majority whites in those states understood that it was not in their self interest to oppress blacks. It wasn't in the self interest of southern whites to do it either, but they were acting out of irrational fears.
This sort of thing illustrates my point. Federal abuses of power affect everyone in the country, whereas state and local abuses affect only those who live in their respective jurisdictions. Those people have more options (like leaving, for example) than those who are oppressed by federal overreaching.