Which Groupset?

To get wireless to work and overcome channel clashes you'd have to make each rider's transmissions unique in some way. Riders could 'sign' their transmissions with a code known only to them, and the derailleurs would have to verify that code on each shift. This would require some kind of code entry system and interface. Fancy plugging your bike into your laptop, or using some kind of display like the Di2 Alfine?

It would make it all massively more nerdy.

Tech already exists though- ANT+ for example, for wireless SRM's to speak to their specific Power Control.