..... Thus efficiency can allow them to steal other firm's customers (since their price is cheaper) but that's all; they cannot improve their margins and thus their shareholder returns via becoming more efficient!
There's another problem that naturally arises as a result when you get down to it: Would you like to make 10% of one million dollars or 10% of one hundred million dollars?
See the problem yet? The insurance company has every reason to promote more claims or more-expensive claims.
It is for this reason that no insurance company can ever be allowed to get involved in price-setting or mandates of any sort.
In the context of cars do you really think the Insurance Institute for Highway Safety (IIHS) has as its goal "reducing the crash rate"? If they have why haven't they done so?
The facts are that they haven't over the last 20 years or so but what they have done is wildly raise the cost of a crash through the mandates they have demanded and got which in turn have wound up increasing the cost of vehicles and especially crash-related repairs.
This of course makes the insurance companies more money -- and lots of it all without a single bit of improvement in operating margin.
EVERY SINGLE DIME OF THAT HAS COME OUT OF YOUR ASS.