In US IIRC, vehicle insurance laws are a State matter, but insurers ensure their coverage subsumes all States' requirements so that driving out of State is legal! The Insurance companies are nationwide and powerful (eg, in lobbying Congress and State legislatures), but tend to use local (State-based) brokers - individuals or companies - who can provide necessary interaction with the State's licensing authorities who issue or transfer 'tags' or year-stickers for them. But it is also a very litigious society.
All which being said, ISTR that a number of significant safety precautions, taken for granted in Europe, were fiercely resisted by US domestic car manufacturers
(because it added to unit costs, and might lead US consumers to conclude that older models without them were inherently unsafe*). But it was insurance companies
' pressure on legislatures which forced States to require them as a condition of licensing new cars. The insurance companies' interest was brutally commercial: the innovations would lead to less costly claims! This process was usually led by California, but other States usually followed swiftly once California law changed. Oh, and once the features were mandatory, the manufacturers made great play in their advertising that the new models incorporated these features, as if it had been their company's idea all along ..
Ironically, Volvo had always included all features used in Europe into their US models also, and included them in their US advertising, and this had if anything boosted their sales among their target US markets (wealthier suburban families).
These features included:
front seat lap belts, then inertia reel, diagonal and rear ones
catalytic converters (and lead-free fuels for them)
day running lights (which used to be illegal in some States!)
air bags, then side impact ones
standardised child seat anchorages
So in US, at least, one could not say that insurers held up their adoption, but rather promoted them.
[*ISTR being told that similar thinking dissuaded Boeing from retrofitting a stickpusher
(like that on Trident) into the 727, staying only with a stickshaker
. This was why there were no 727s on the UK register until DanAir got a bunch of old ones cheap, and paid to develop and certify a -pusher mod to satisfy the CAA. Happy to be corrected]