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There really isn't any reason to not vassalize him. He can't call Crusades or the like, and I believe the only "invasions" he could grant would be against other Miaphysites. Which, if you're Nubia or Abyssinia you've probably already conquered the other and Armenia has long since fallen, and if you're Armenia odds are Nubia and Abyssinia have long since fallen. Not only that, but having him as your vassal should give you even greater range to excommunicate people.

So no, beyond maybe RP reasons there isn't any benefit to not vassalizing him. Then again, RP reasons are always valid reasons if the goal is simply to have fun and not try to be as disgusting of a blob as possible.
 
If you're miaphysite yourself, do it, because it means that you can use a 'carrot or stick' approach to your own religious head. Regardless of whether they call crusades, it's still beneficial to vassalise your religious head.
 
Well, it's all about where you stand in the Emperor vs Pope issue, only in Egypt/Armenia instead of Italy. You always play the politician so it's safer for you if the Pope is your vassal, but if you're a zealot pious generous guy, it would make sense to give the Pope his independence.