I'm pretty sure this is why Jim wanted to keep certain perfomers exclusive to certain entities within his organization - so that way, there would always be a decent amount of performers free and on hand to perform in a project whenever he needed them; this is why up until Jim's death, we never saw Dave or Steve perform on SS, and similarly, obligations to perform Big Bird and Oscar basically made Caroll exclusive to SS.
Honestly, this is why I feel like Matt wasn't a logistically wise choice to become Kermit's new permanent performer, given he's already got a full plate with doing Big Bird full-time now, but also taking on almost all of Jerry's characters, and even how he's far more involved behind the scenes of SS these days with directing and training new performers. Yes, Matt's an amazing and versatile performer, but he's only one in a pool of performers they could have gone through.