It's part of that. But also that it started as markettability: "car x is safer as car y so if you care about your life, you but car x".
Later this got put into law (Health insurance costs, disabilities, people being taken out of workforce, political popularity: "He cares abour our safety", people who care about the lives of those who don't care and could drive reckless, ...) and later insurance companies who need to insure for less injury or death (and those who stay behind like women and children without a "caregiver" in the few traditional homes left). And as you point out the safety of other drivers who get impacted of your driving stupidity (crash impact).
And perhaps some personal motivations of people in the entire line of history losing someone left or right in an accident and "wanting to prevent the preventable".
I don't think these things are in place out of selfish reasons, nor a conspirist undertone, nor are a form of "silencing the people" or "taking responsability away"; it's an organic process of many linked and related people trying to do good (wether that means for themselves or for a higher, personally defined, purpose.) the same way you go to work and do your thing.
It's intelligence of crowds and the current time-spirit. Nothing fancier.