Emma in the Avengers would be a terrible fit- for her. She's above them, and it would offer nothing new to the character.
Actually, the original plan was Xavier, then Magneto. Maybe Emma was a 3rd choice, but even then, she wouldn't make any sense in the book. You can just buy that Xavier would leave his Infinity Gem to Beast (at the time at least, not now), but certainly not to Emma, specially with X-men he was much closer to available.