Thanks for being understanding and engaging in good faith :)
I think making vaccines legally mandated is an interesting discussion. On one hand, I think they should be mandated for reason that they are, statistically, proven to reduce overall harm to people. On the other hand, it think it's a bit scary to go that way, since we are then putting a lot of trust in whatever political body will decide which vaccines have a risk/benefit profile that should make them mandatory. It's a lot easier with seat belts or construction practices, since there are literally no downsides to either.
I've had a thought experiment with others about a hypothetical autonomous car that is guaranteed to never end up in (or cause) any accident, but has an astronomically small probability of spontaneously combusting at any given moment. Let's make that probability small enough that the number of deaths and injuries caused by cars every year is reduced to 1 % of what it currently is, with the remaining incidents being caused by the spontaneously combusting cars. Now, for any individual, it's statistically safer to drive this car. As a society, everyone is safer if these cars are mandated (no pedestrians are killed, we don't need to spend healthcare resources on car-related injuries, etc.).
From a utilitarian perspective, these cars should be mandated. From a purely logical risk-minimisation perspective, everyone should be jumping at the opportunity to use this much safer car. However, when you ask people, it turns out that most don't want the car. Despite knowing that this car would (statistically) drastically reduce their probability of being hurt or killed in traffic, the idea of getting into a vehicle that can spontaneously combust at any given moment seems absurd to them.
That brings us to the "Twinge of doubt for something that has been so successful". We humans are generally terrible at risk assessment. We tend to heavily over emphasise extreme outcomes (the car combusting) while also under emphasising "mundane" outcomes (people crash and die every day, but it surely won't happen to me), and overestimating our own skills (by far most drivers think they're above average, and can therefore avoid collisions). The analogous vaccine-related line of thought would be that people hear that 1 / get severe complications from vaccines, which is over emphasised, while "hundreds of people in the US are killed by tuberculosis every year, but it surely won't happen to me", and overestimating our own immune system.
Basically, a lot of fear is simply irrational, and that's linked to the human nature of being crap at intuitive risk assessment. I think fear of vaccines also falls into this category of irrational fear, and I don't really think it can be rationalised away. That's why I think programs to counter vaccine scepticism need to be based in how to make the rational fear of disease win out, rather than trying to completely dispel the irrational fear far too many people have related to vaccines.