I think that cup should be changed, but on a different way.
There is a lot of teams in the low leagues. In fact a majority of the teams. So there can be created cup, played just between teams from 6. league separately, 5th league separately, 4th league,.. so do a division way of the cup. Higher league can play more matches against (home and away) as they are closer to the final, so there will be same volume of matches, so you can compensate lower volume of teams in higher league... this would continue like that into secon leagu where would be probably whole season like two matches to go against next team and first leagues can play international cup against teams from the countries with similar volume of users.
That way would be possible to have a chance to win a cup to everyone, not just to 1st league teams. That seems to me pretty boring. And what is normally cup about if not about trying to win that?