it's an interesting problem, of course the dangers of vaccines are not secret, whenever you get your children vaccinated you get a packet of information that discusses all of the reported adverse reactions and their likelihood, for example

"Shoulder Injury Related to Vaccine Administration"

The most common adverse reaction is something that is a possible reaction to any shot because you are sticking a needle into someone's arm, multiply that by millions or hundreds of millions of people and some of those will get infected or the person will be allergic to the vaccine or some ingredient in it or the nurse stabs a nerve or whatever. There would be these events even if you administered saline solution to as many people as get the flu shot or some of these other vaccines.

In some ways it makes sense to have these protections for industry as frivolous lawsuits could make it impossible to do business, similar to how gun makers have protections from certain types of lawsuits because otherwise stupid assholes would file endless frivolous lawsuits that they could not afford to defend themselves from and the gun industry would simply go out of business. you are right though that the danger is that these protections disincentives them from creating the safest possible products.