Well said. I've already decided to get the vaccine, based on the same kind of sound reasoning you have mentioned.
But I would say that many people taking the vaccine are of the belief that there is no risk, which is the messaging of the pro-vaccine side. It seems strange that we have to lie a little to get people to the right thing. But once in a while, those lies backfire. Which then creates doubt the next time a group of experts gives us advice.
I have written about the perils of fear-mongering:
http://www.tiereddemocraticgovernance.org/blog_details.php?blog_cat_id=25&id=43