This is not a good analogy.
Aircraft manufacturers and airlines have a lot at stake if they let any risks slip through. If anyone dies it will be big news and visible to everyone, with real consequences for the companies responsible.
(I'm in the US so this may only be relevant there)
Childhood vaccines could cause a serious chronic disease in 1% of kids and we would have no way to know because:
1) Many vaccine clinical trials only monitor outcomes for a few days to a couple weeks.
2) Most vaccine clinical trials have no placebo control. If they have do have a control group in most cases the control group gets a different vaccine.
3) Most kids in vaccine clinical trials are also getting 10-30 other vaccine injections during their first two years of life during the period that they're being monitored for the one vaccine in their trial. So the only way this could even produce a signal would be if the one vaccine under trial was the only one that caused harm and all other vaccines did not.
I am not saying that vaccines do cause chronic disease in 1% of kids - just that it seems to me we don't have a good way to know.
Furthermore, even if it was proved that vaccines caused harm, vaccine manufacturers are not liable for harms from vaccines on the childhood vaccine schedule.
It's a very different situation from flying.