Yeah, I imagine that. I just mentioned the lower leagues because that's all I've experienced so far :P. The "higher division team plays away from home" would maybe even the field, but perhaps at the expense of other things.
As we've agreed, the cup is a delicate thing and I think the way things are works out fine. Another idea would be having a cup for "higher leagues" and another for "lower leagues". It might be more competitive and allow for more desirable revenues, but may bring different issues. It's just a thought, I'm not sure myself it would be a better way to go. Cheers