This cup would be played by all teams of each division playing in the same country, a cup of very low importance, only thought for let to the small teams win money with the tickets. This cup doesn’t replace the current national cup, both would be played being the current cup obviusly the main tournament cup.
As you can imagine, top level teams only can play as much 4 matches if they reach their cup final, but a team placed in, for example, D division, can play 9-10 matches because there are many more teams in D division. Lower division, more teams and the possibility of play more matches. This cup let to small teams to have an additional income for be a little closer in economy terms to the best teams of the country and gives to everybody the chance of dispute another cup.
The factor fatigue and training would be minimal, of about 2% fatigue and only a 10-15% of training than in a league match because top level teams only can play 4 matches as much, there wouldn't be economical prizes for the winners. I insist that the only goal of this idea is to let winning money in ticket selling to the small teams and give them another motivation in the game.