There’s more risk of being in a car crash, we don’t go into any of those statistics when buying a car, or getting into one.
Well some people do, NCAP ratings for example are consumer crash tests performed on new cars, and rate how well the car protects occupants (driver, passengers) and also pedestrians if a collision were to occur.
Not everyone wants to look at NCAP ratings and there are legal minimum requirements for that reason - any new car you buy in a rich country with good infrastructure and regulations is going to have as a bare minimum, things like seatbelts, lights, airbags, ABS, isofix to fit child seats easily etc. Probably other things that benefit safety but that we take for granted or don't think about because the details are quite technical. And in the UK we have MOT inspections to ensure that the car is still safe to drive even when it is not brand new. We also have regulations built into new road and junction design, signage and signals which help to ensure that where there is a higher risk for a collision, things like visibility and redundancy are built in so that if someone does make a mistake while driving, other drivers have the chance to notice and react to this without causing a further hazard, so it is less likely that someone will be in the wrong place at the wrong time and have a crash, even if someone does do something wrong.
As a result, car crashes are both rarer (per mile/km driven) than they used to be and less likely to result in death or serious injury when they do occur, and this improves all the time as older junctions get upgraded to newer standards and older vehicles with fewer safety features leave the road.
Healthcare could be the same - rigorous standards to ensure a basic level of safety and efficacy can be assumed so that if you're not bothered about the details and just want the summary of what's recommended - you can do that. I believe this currently works well for the most part, and if you feel flummoxed by any medical decision, it's almost always a good idea to follow the recommendations set out by NICE, WHO, unicef etc.
However, agree it is helpful to have nuance in the discussion and transparency for those who are interested or worried. Just not so much to have that displayed as the first line - it's very unclear and confusing. It does make sense for the first line communications around public health to be clear and simple, with access to more detail if people want it but I think it's OK for this to have to be actively sought out.
The thing is I do think this is better today. When DS age 17 was born, that was the first time I had ever come across any suggestion that vaccines might not be safe and effective and it scared the crap out of me. Back then, there wasn't much from the "official" sources or at least I found it difficult to find, whereas I had antivaxxers falling over themselves trying to bombard me with so much information that I was falsely reassured (that not vaccinating would be the safer choice). The discussions online are far too polarised, I agree. Trying to discredit antivaxxers using ridicule is unhelpful because it drives people right back to those same sources of misinformation because they are validating of your fears (which they often stoked in the first place!) and offer (false) certainty.