I have familiarized myself with various definitions (one-dimensionality of simple left comodules, generated as an algebra by group-like and skew-like elements...) and examples of pointed Hopf algebras (small quantum groups, universal enveloping algebras of Lie algebras...) but I have yet to get an intuition for how the pointedness of a Hopf algebra affects its structure. I know there are several open questions about the structure of pointed Hopf algebras, but can anyone offer an explanation, perhaps with an example?

(I have seen the other posts asking basic questions about pointed Hopf algebras, but they didn't quite address my question.)