One of the things that was so astonishing about the original Secret Wars was how it was so totally dominated by the personality of Dr. Doom. "Secret Wars" was basically a Dr. Doom story.
I'm also intrigued now with what is going on with Dark Reign, which features Norman Osborn in a way that is many things, but is definitely not out of character: one thing I always liked about the Green Goblin is how unlike other super-villains, he actually had (and kept!) a secret identity.
For a crossover, you'd have to have a villain that fits three criteria: 1) They have to be threatening and powerful, 2) they have to be reasonably well known, 3) have to have well developed motivations (because their motives and actions take center stage).
A poor choice for something like this would be Galactus: sure, he is threatening and scary, (#1), he is reasonably well known (#2) but being so remote and unknowable, his thoughts and feelings are entirely opaque to everyone. For that reason, despite the very high-stakes nature of the Celestials, they too would make poor choices for a crossover villain.
Likewise, I think part of the reason Secret Wars II wasn't received quite so well is because it was the story of the Beyonder and the Molecule Man...and that's a clear-cut violation of seniority! No wonder the Red Skull seemed so cranky in the years following that.
By contrast, crossovers can have non-senior or traditional characters take center stage. That's just more proof that if you're a slacker, you can ignore your hero as long as you focus the attention on the villain. I always liked how Captain Marvel and Starfox seemed to have such important roles in the Thanos War. Likewise, all the Infinity Gem series were centered around a character like Adam Warlock, who is a good character but a very strange choice to be the central figure of a huge company crossover.
It's intriguing how Magneto hasn't been tapped to do a crossover...well except for House of M, which was an alternate universe story so it doesn't really count. Magneto is famous, has a well defined motive and personalty, and is so powerful and threatening that he's a one man nuclear nation, treated as a fact of life in international diplomacy.
I'd like to think the Red Skull, too, could be a big crossover villain, as he is an insane master-plotter and mastermind.