I've heard it argued that simply thinking of a new problem should be sufficient for patent protection, though I strongly disagree with that position. Put differently, identifying the problem can be significantly more difficult than creating the solution, but I still think patents should cover non-obvious solutions to any problem, rather than any solution to non-obvious problems.
Absolutely, only a non-obvious solution to a problem should be patentable.
But if they at least only granted patents to specific almost-obvious solutions, and not just to any solution (which is the same as patenting the problem), it would be a little better: You could at least try to find a different solution...