What I'm not seeing is engagement with the actual text of the statutes that Congress already wrote and put on the books. For instance, the OSHA Act specifically gave OSHA power to regulate "new hazards".
https://www.govinfo.gov/content/pkg/USCODE-2019-title29/html... "1) The Secretary shall provide, without regard to the requirements of chapter 5 of title 5, for an emergency temporary standard to take immediate effect upon publication in the Federal Register if he determines (A) that employees are exposed to grave danger from exposure to substances or agents determined to be toxic or physically harmful or from new hazards, and (B) that such emergency standard is necessary to protect employees from such danger."
Similarly the Social Security act already gave broad power to issue regulations. https://www.law.cornell.edu/uscode/text/42/1395hh# "such regulations as may be necessary to carry out the administration of the insurance programs under this subchapter" "No rule, requirement, or other statement of policy (other than a national coverage determination) that establishes or changes a substantive legal standard governing the scope of benefits, the payment for services, or the eligibility of individuals, entities, or organizations to furnish or receive services or benefits under this subchapter shall take effect unless it is promulgated by the Secretary by regulation under paragraph (1)."
the Act clearly envisions the secretary having authority to change standards for benefits, payment for services, and eligibility. There's no limitation saying that eligibility criteria can be based on other safety measures, but not vaccines.
EDIT: and SCOTUS precedent interpreting this language in the past was clear about the scope of authority it gave. See page 34 of the PDF here https://drive.google.com/file/d/1dGiMcVAxfziaoecQtd40-nERZr_...
A mandate for vaccinating healthcare seems a lot closer to existing regulations that the law was designed to allow. It’s clearly a health and safety regulation just like the dozens of previous health regulations regulating quarantine, mask wearing, sanitation, safe handling of items, etc.
The reason congress doesn’t reserve this power is because in our system congress can’t react quickly or sometimes at all. It has to pass laws giving up this type of authority to the executive branch because it knows its own processes don’t work quickly or efficiently enough.
Congress did give itself instead the authority to veto regulations it doesn’t like, using the Congressional Review Act. It used to give itself even stronger authority using the one-house legislative veto, but the Supreme Court struck that down. < https://scholarship.law.duke.edu/cgi/viewcontent.cgi?article...>