I think we're losing sight of the issue here. I'm not talking about eliminating the cup, or anything as drastic as that.
There's a clear advantage to some teams and a clear disadvantage to other teams, as a result of the random cup draw. That's not up for debate - it definitely exists. Whether you think it's a big deal or not is debatable, which is fair enough, but it's undeniable that the disadvantage is there.
A seeded cup draw makes it much fairer, as teams in the same league will on average face teams of around about the same strength. This removes those instances where teams get significantly easier cup runs, thus removing that big advantage.
I'm not talking in absolutes here. Obviously teams can still be eliminated earlier than their league opponents and I'm not suggesting at all that this shouldn't be the case, nor that this is unfair or bad for the game. My suggestion is aimed at removing the obvious disadvantages placed on some teams as a result of something completely random.