After all, those problems are on the edge because they're difficult to solve given the intellectual tools we have today.

That doesn't seem obvious to me. If you were to look at a map of the known world drawn by a member of an ancient civilization, I don't think all the edges of the map would be regions that were particularly hard to traverse. Maybe they'd be the edges just because they were far from the civilization's population centers and no explorer had wandered that far yet.

In a similar way, perhaps the boundaries of our knowledge are what they are just because to reach the boundary and make progress, you first have to master a lot of prerequisite concepts.