Given that the Cubitus is intended to be a sports watch, I would imagine that implies it will focus on automatic-winding movements. I am sure that a square-bridged version of the micro-rotor movements could look appealing, I am not so sure about the center-rotor movements. Would a square movement with a circular rotor look nice or would it look jarring? I suspect the latter.
I would not be surprised if there were thoughts about making a square-bridged version of the 240 for the 5822 at some point. However, I think if Patek had launched a 5822 with a square movement but the 5821 with the round movement it would not have pleased too many people.