There's no guarantee that anyone's premiums would actually go down. Instead, you might find people that thought their premiums would go down actually go up because of this. After all, we're talking about insurance companies who are the poster child for fucking over their customers. Giving someone this much visibility surely means they could find something to justify a premium increase.

I would never voluntarily submit data to insurance like this. It's a suckers bet.

Total premiums would only go up if total losses go up. Simply disclosing more data would not cause total losses to go up.

Insurance pricing is very competitive and if one company raised premiums without experience by more losses, another would come in and offer insurance at a lower price.