I'm not sure what you're getting at, Congress gave the agency the power to set guidelines for requirements for caring for medicaid/medicare patients, that's what they do. If a guideline would not actually impact medicaid/medicare patients, then they can't do it and it would rightfully get struck down in court when it is challenged for not falling within their powers. That's quite literally the same mechanism currently being used to challenge their power to require vaccines.
Your point about natural immunity seems reasonable, it doesn't mean requiring vaccines for those without natural immunity wouldn't still make sense though so I don't think it really fits your point. Claiming that the particular way they went about this requirement is bad is different from saying they can't require a vaccine at all. I think your point makes some sense, but it could still be paired with a vaccine requirement making it effectively the same thing.
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I thought what I said was pretty self explanatory. If Medicare and Medicaid are going to be worth it then we have to have some standard level of care that we're paying for - we shouldn't be paying tons of money just for medicare/medicaid patients to receive bad care. Why should my tax dollars to go a healthcare provider who doesn't want to get the vaccine when that money can go to one who will? The medicare/medicaid patients that we're paying for will get better treatment from those healthcare providers who require vaccination, and if better care is not the goal than what is?