Yes, it is extra games, and can cost you time and points, but, notwithstanding all of that, I think that clubs from lower divisions regard the cup as an adventure, and reaching quarter-finals, or semi-finals, or, even the final, as an astonishing achievement.
This is what the romance of the game is all about.
Personally, I love to see them do well, although, experience has unfortunately demonstrated that if they do succeed in reaching the finals (unless you are merely one division lower, and, these days, even that is usually a proverbial bridge too far), that this tends to give rise to a regrettably rather one-sided contest.
However, the cup also generates income (very welcome income), for lower division clubs, and gives them valuable experience of playing against higher ranked teams (plus confidence), and serves to help build club traditions, myths and legends, especially if they obtain a result (a draw, a victory) against a higher ranked club.
And, it does allow space for experiments, trying out new things, in players, positions, tactics.
