Not at all. If you have employers that say get the shot or you're terminated, the person who doesn't want the vaccine will lose their job.
This is why several states are already passing laws banning this.
You keep bringing up hospitals and healthcare jobs. But vaccines come with the territory in those jobs, and vaccines were required when you applied for those jobs. So it's not the same thing. If you are very much against vaccines, don't work in healthcare. That's fair enough.
But now say at some point Disney World requires all cast members to be vaccinated. What do you do with a CM that worked at WDW for 20 years, who's against getting this vaccine, refuses to get it? Getting a vaccine was never part of the job requirements when they were hired. No reasonable person when they took a job at Disney World believed a company would be so intimately involved in a employee's own health decisions.