Part of the wonderfulness of Religion is that it requires faith. It is not based on logic or proven concepts. It is literally a leap of faith. Which is the cost of entry. I personally believe impossibilities like you quoted where guided by God to sow doubt and help establish the faith requirement. Because free will is a thing and you have to decide of your own accord to believe. If I could snap my fingers and prove my faith beyond any shadow of a doubt, then it wouldn't be worth anything, because a measure of faith and trust would no longer be required. There is a logical science side of human nature and their is a vast spiritual side of human nature. Both must be nurtured and supported in harmony, not opposition.
As far as public health....why? By all available facts and your own posted positions, if you have the vaccine and booster you are safe (which the majority have at this point). You are 99.99999% not dying from COVID. So why do you care.....let people make that choice with their own bodies and go about your day. Some even take the Darwinism view and are happy about it, as those who are dumb are dying off (which is fine view by me, if a little morbid). At this point the vast majority of un-vaccinated are aware of the risks. Same with smokers......they all know its bad but some still choose to partake. Again, if I could snap my fingers and everyone in the world was 100% vaccinated......guess what......COVID would still transmit and there would still be a background level of deaths. So the public health argument does not hold water. We don't shut down the entire highway system when the occasional tragic accident happens because as a society we have deemed that an acceptable risk to living life and productivity.