Literally CNO's job is to man, train, and equip- and that's the law too.
I think what you're really asking is who talks to who and what do they say when someone says they want another aircraft carrier deployed next year, but the answer is yes you can have an aircraft carrier but no, it's not going to be able to do everything it's supposed to do because lots of stuff is still broken or worn out.
My point is although the service chiefs don't control the operational requirements since the COCOMs do, shouldn't the CNO be pushing back and saying the debt we're going to incur long term debt by operating this way which is going to lead us to more problems in manning, training, and equipping the force? In the wake of the C7F collisions, there was a lot made about ship COs not feeling like they could say no to a requirement without getting fired, yet I haven't heard any CNO in recent memory give pushback on similar demands at a larger scale.
I faintly remember Jay Johnson doing so, but my memory might be clouded.