The Higgs and black holes are quite different. We've basically observed Higgs according to how we've defined them, while we've only observed phenomena consistent with black holes as we hypothesize them. Singularities are the result of theories based on (ironically named) real numbers, it's entirely possible that what we call black holes are really dark stars formed from exotic matter that can only exist in hyper-extreme conditions, like a leveled up neutron star.