Any useful coronavirus vaccine has to work for the vulnerable people anyway, the old, the obese, the diabetics etcetera and these would be the people with a valid reason.
If these people can get vaccinated everyone can choose, get vaccinated or run the risk. I don’t care. And there is no herd immunity story.
First, many people with relevant "underlying health conditions" don't know they have them yet.
The public warnings talk about visible things (obesity etc) because they are the only ones it is useful to publicise. It doesn't mean they are the only relevant conditions.
Second, Covid-19 strikes down many healthy people, and "long covid" is an awful long-term disability.
Third, vaccines aren't perfect at an individual level. Their use tips the balance to the disease dying out, but they don't confer perfect protection to every individual that is vaccinated. People still depend on each other, so herd immunity still matters.
If individual people don't want to get vaccinated, it's not just their problem.
It contributes risk to everyone else, by pushing the R number higher, increasing the size and duration of clusters, and potentially tipping the balance towards permanent pandemic instead of the disease fading out.
That's the point.
In light of that, "as long as they don't ask others to keep the infinite quarantine" doesn't make sense. If lots of individual people decide not to get vaccinated (assuming there's an effective one), they won't be the ones asking for stronger quarantine.