It does, just not by much if you look at individual cases. But insurance companies don't look at individual cases, they aggregate risk. And if millions of people buy carbon neutral HVAC systems, it will definitely decrease aggregate insurance liability for hurricanes.
The flaw in your original argument, and the reason we don't generally see insurance companies on the front lines lobbying for positive changes for consumers, is that they have the option of simply raising their prices in response to the risk landscape, rather than trying to change the landscape itself. This is why free markets, as useful as they are in many contexts, can't be relied on by themselves to provide a healthy, stable society.
There's not any single insurance group large enough where the aggregate risk of climate change is even remotely within the possibility of affecting change.
The IIHS represents the interests of 94 percent of vehicle insurance policies on US roads. So, almost all of the cars on the road are under underwritten by policies of IIHS members. Any change they affect has a direct impact on their bottom line.
There are a few property insurance trade associations in the US, and I don't think any of them have quite as high of a membership representation as the IIHS does for auto insurers, but let's for the sake of argument, say that there's an association that represents a full 100% of homeowner and commercial property insurance policies.
If that existed, they would have influence over 13% of US emissions, or ~778 million metric tons of CO2. But, while insurance law does stay within a country's borders, CO2 doesn't. Global emissions are 35 billion metric tons. So this hypothetical super powerful trade group would have influence over 2% of the total. If they could impose an (extremely expensive) requirement of a 20% reduction across all of their policyholders, this would have a 0.4% reduction of the global CO2 emissions.
Basically, assuming the most powerful trade organization possible, it would have no real effect.
International cooperation is required to fix this particular problem, and insurance just isn't an international-scale thing. Treatises are going to be the only way to fix it.
So, I guess we shouldn't thank them so much. Climate change was only one of the many items the insurance industry isn't helping much with. Which is my point. And I don't think they were particularly instrumental in getting the automotive safety ball rolling, either, though I'm sure they were happy to join in once it was.
For sure, it is a happenstance of aligned incentives that make the IIHS relevant.
That’s being said, they were a significant proponent that accelerated most of the safety improvements in North American vehicles since the mid 90s when they started doing overlap crash testing.
Before that, governments were mostly complacent with full-frontal crash testing, which simply wasn’t realistic enough.
Most of the major changes in North American vehicle safety has been due to their efforts.
Now, they’re not altruistic, they’re just asshole insurance companies with the right incentives.
Those other issues are obscured by tragedies of the commons.
If you install a carbon neutral HVAC system in your Florida home, it doesn’t decrease your probability of hurricane damage due to climate issues.