I'd never really thought about it, but in a capitalist society like the US, this is how you really determine how safe something is: how much does it cost to insure?
Insurers are on the spot financially. If they get it wrong, it comes out of their margins.
Ultimately, you need insurance to be on the road. If you cause an accident, the other side will want to see some money. That's why insurance is mandatory: to make sure that money is there. The price of the insurance is directly correlated to how likely you are to cause an accident. Insurers use all sorts of criteria, including how young or old you are and how much claims you've made before.
Insurers noticing that they get a lot less claims for self driving cars is going to pretty soon lead to price differences for people who still choose to drive themselves. Cars without self driving features are going to be more expensive to insure. Liability with self driving cars vs. manual drivers is also going to be different.
As a minor point, there's nothing inherently capitalist about it - the largest personal lines auto insurer in the US (like many of the smaller ones) is a mutual company, meaning that it doesn't have outside shareholders and functions more or less as a cooperative owned by its policyholders.
It turned out that being a fire fighter was extremely dangerous, so insurance premiums were costing more than equipment! Underwriters Laboratories started producing literature on how to make fire fighting safer, and now NFPA has turned that into strict guidelines that fire companies must follow or lose out on insurance claims.
For example, fire fighters now must ride inside the cab. No more hanging on the back (falling off the back was very common, causing many severe injuries). Seatbelts must be worn inside the cab. An SCBA must be worn inside any dangerous atmosphere. Turn out gear must be inspected after every burn, and replaced every ten years. The list goes on.
Finally, there is now a whole new branch of study called "fire dynamics" that is all about the science of fire fighting. UL regularly performs experiments at my local academy to test various techniques on different types of building fires. They will instrument a whole building, then start a fire a certain way, and measure what happens with different techniques. In just the last ten years they've changed a lot of former "best practices". For example, they now recommend what they call a "transitional attack" where you shoot in a few seconds of water through a window from the outside, then make entry. This is proven to greatly reduce heat in the building and allows for a better chance to put out the fire vs just running straight in. This has been a huge upset in my area, with a lot of the older folks thinking we should just always make entry ASAP. However, it is proven time and again that transitional attack is optimal in most situations. The few seconds "wasted" is proven to actually make fighting the fire safer and more effective. It is counterintuitive, but it works.
All this because insurance was accurately calculating how dangerous fire fighting really is.
Of course, there is a flip side to everything. A lot of the "fun" of fire fighting is now turning into "rules". Hanging on the back used to be an exciting reward for showing up even if it was a false alarm. Breaking all the windows at a house used to be a fun thing to do before UL found that it makes a fire significantly more dangerous. As the profession matures, we're faced with less personal agency and more checklists and paperwork. This is destroying volunteer fire fighting. Most of the US is served by volunteer fire fighters. As it becomes much harder to keep up with the rules and paperwork, volunteerism is dying. Many companies across the nation are on the verge of collapse because no one wants to volunteer. Between the rules and the cost of living crisis, almost no one has energy to show up.
So nothing comes for free, insurance made fire fighting much safer, but now it's much harder for volunteers, which are the majority of the fire service.