There are some who are reacting as you say, and the result is that paediatricians who serve their nonsense are being (IMHO deservedly) struck off. Measured across the state, the effect is that the deaths caused by the selfishness of those who wouldn’t take vaccines or, worse, chose to lie about them, have fallen significantly; it’s that effect that I consider worth focusing on.
There’s a perfectly valid question about the American healthcare system, and the ridiculous costs it causes, but that is something that no state can address significantly because of how the USA is set up. Meanwhile, compulsion starts to emerge because the simple, calm, and adult conversations you support are subverted by the sort of cranks and charlatans who promote anti-vaxx, Great Reset, 5G and other sorts of anti-scientific nonsense. The tragedy is that when they start lying and myth making, they create the climate of hype that makes those sensible conversations almost impossible to hold.
I use it, as I’ve repeatedly said, as an example of where it’s a policy that has worked to achieve a particular health objective, and where for all the noise about “compulsion”, the courts have upheld the legitimacy of the policy on human rights grounds.
Whether it’s relevant to Covid, I don’t know. I hope that enough people do take the vaccine that the question becomes academic, and that the damage it does gets suppressed by the benefit of vaccines across the population, here initially and then worldwide.
As for your final question, I’ve no philosophical issue with childhood vaccines being made mandatory and access to public facilities including schools being part of the enforcement process; if Covid vaccination were authorised for children then I’d have no more issue with a child of mine having that than I did with their other childhood vaccines. My questions would be purely practical, and about whether the policy would make a material difference to the incidence of and damage from the disease being vaccinated against.
More generally, I simply don’t understand the logic that vaccination for a disease that carries no moral baggage for the infected is such a private matter that no one else has any legitimate interest. As John Donne wrote: