Because they (wrongly) allowed delegation of "all legislative powers herein granted" in the first place, and now they are stuck with the consequences.
My point was that the courts might decide that delegation is fuzzy, and should be fuzzy. Meaning it is fine if more than one agency is “in charge” of a particular aspect.
The CMS mandate covers workplaces subject to OSHA, so overlap is inevitable.
SCOTUS can get out of the trap by allowing MORE delegation, in the form of fuzzy statutory law. Then the question of “is this the right agency” is settled thusly: there is no such thing as the wrong agency when it comes to asserting federal power.