Yes, great idea. There could be the canned unrated problem sets for each ECO code (all 500 of them!

) for problems which are on move 20 or less. And the search parameters for making your own problem set could allow you to choose a range of ECO codes and the maximum move number in the game (10 or 15 or 20 etc.)
Maybe a better indicator of whether the problem is still related to the opening is not the move number, but the amount of material still on the board.