Really? Not safe and effective? So what about polio? Did it just up and disappear?
A double blind study is not the only way to study this stuff. Longitudinal designs would reflect a relationship if there was one to be seen. But at this point there isn't one. And the way you state your analogy is way off. The vaccines have been researched for efficacy more than what you're saying. Based on your argument, Black Diamond should get a bunch of climbers together and have them do fall tests because somebody thinks double-backing their harness causes a skin infection with a double blind method of not allowing some to double back the buckle.
I'm curious what you would propose? A true double blind scenario? So essentially risk the lives of children when no evidence warrants it? And even then, the results would be skewed due to the effects of herd immunity. So do a double blind study and give everybody a dose of smallpox to test the vaccine? If your kid croaks,surprise, you got the placebo! Seriously though, you're dwelling on that one method when there are plenty of other research models and statistical tests to evaluate the effectiveness and risks. The reason you can't find a study you're looking for is because they aren't done at that level very often. If they are, something really warrants it and the conditions are very different. So again, why go through the expense, risk, work, risk, time, risk to do a study that nothing supports doing? Plenty of longitudinal data and experimental designs showing effectiveness and risk lower than the repercussions. A double blind study does not have to be done to show this.
Also, you can go to pubmed and type in "human vaccine efficacy" and see the a snapshot of the work being done and choose which one shows data that they are effective means against some conditions. And those that are on binding, delivery mechanisms, etc will likely have plenty of cited sources in their review of literature. Take your pick. And I'm sure you can find data on infant mortality rates, survivability, and all sort of other relevant information. And if you have a viable source citing the risks that are popular to claim right now, please post it, as I've yet to see one of those that hasn't been torn apart. If the data truly supports it, I'd be more than willing to change my tune. I did a paper on incentive spirometers in nursing school just because I started finding data that they weren't effective in many of the cases they were used. Instructors weren't happy about it and talked to me about my patient care, but I had the data to show them. And they backed off and changed their emphasis.
You are completely correct that all medical procedures carry risk. A simple IV could lead to an infection leading to sepsis. And there is an off chance that a med won't be effective--like birth control. But courts aren't a viable source of the efficacy of the drug. In the same way small guys can get buried in the system, lenient courts can overlook facts and data because the rules of the law are well plaid. Why do you think a lot of people don't like practicing medicine in certain areas of the country-- very "generous" juries regardless of the facts.