Lists of Unsolved Problems

Would it be useful to have classes for unsolved problem analogous to the complexity classes for algorithms?

The class of problems...

... informally posed but lack definition

... formally posed but lack framework

... framework exists but there's no solution method

... solutions exist with modifications

... sidely accepted as true, yet unproven

Of course this would no longer be rigorous mathematics but an epistemic heuristic. One could for example study the most common transitions from unsolved to solved.