Unforunately I came back to this long after the edit window, but it occurs to me to clarify #1. One of the reasons we like hash-based signatures despite the fac

Unforunately I came back to this long after the edit window, but it occurs to me to clarify #1. One of the reasons we like hash-based signatures despite the fact that hash functions are not versatile for PKE/KEM is because they're very simple and performant. Hash-based signatures don't require advanced mathematics to understand; an elementary knowledge of discrete probability theory and general complexity theory is sufficient. Contrast this with most proposals for quantum resistant schemes, which require a significant understanding of linear algebra and {group,ring,Galois} theory. In the case of isogeny-based systems, add more number theory and algebraic geometry to that list.