Why didn't Elphaba make Glinda into a broom?

Like Glinda would still be a regular human but could float around like a broom and hold her arms out like "wheeee!!" while Elphaba flies around riding her. There is foreshadowing and hints that Glinda would love this, such as the scene where she hangs on the chandelier because she loves to be in the air. It would also solve the "Glinda has no magic" thing because she would be useful as Elphie's magic means of flight and could fly on her own. Bonus, with the cape draped over them both they would look like a majestic two-headed witch creature and I think that would make good fanart.