Nobody says we must maintain some "pure" system. For an already existing example, passing a constitutional amendment is far, far more difficult than regular legislation. Is that undemocratic? By the most "pure" definition, yes. It's far from just letting everything be decided by 50+1 popular vote. Or hell, even the fact that we have representatives we elect instead of using direct democracy for everything.

Limiting democracy doesn't mean just installing a dictator or something. It can be as simple as placing some issues beyond the reach of majoritatian whims. I never see any of the people crying about democracy upset that their free speech isn't under question of majoritatian will.