Saying all disciplinary actions are on the table is a statement intended to scare folks into submission. A.K.A., a threat. The threats my CO have given are just a more exact elaboration on what disciplinary actions could be taken.
You can say that about the UCMJ and orders in general if you want to be that broad.
Sure, that justification can be used for sea-going billets. If that were the goal, it could be a part of one's pre-deployment physicals. But military leadership isn't mandating the vaccine... that's Biden. Military leadership are, however, deciding to require it for folks separating within 180 days (the only vax these individuals can be required to get in this time frame), to deny exemptions, and to threaten severe punishments. Tell me again how requiring my friend, who will be on terminal leave when the mandate deadline expires, helps Navy readiness by getting the vax on his way out?
It does nothing for the military when a very significant portion of the force would not be deployable on short notice, and would not be for up to a month or more if folks had to get most of the vaccines available to deploy (two shots with a two week period afterwards for full efficacy).
Readiness is not only about worldwide deployability though and includes ensuring the entire force is as healthy and ready to perform their duties in general no matter where they happen to be in the world.
Finally, the military was moving forward with mandating the vaccine well before the President mandated it.