Mid-market insurance has a sort-of-a use case, but I've not quite been able to make it work (yet).
If you are a large-ish business, you will talk to your insurance broker to insure it. This will probably turn into a multi-thousand page document describing all the assets that you want protected, and what events you want them protected from.
The broker then does "marketing" which means nothing like what marketing means in any other context. It means that they are going out to the underwriters and asking them what parts of that whole package they are willing to underwrite, and at what costs.
The broker then cherrypicks whatever is best for their client by piecing together underwritings for different parts. ("Allianz is underwriting the buildings for the first $800m, Lloyds will do everything beyond that up to $3B, SwissRe had the best weather insurance...") The client wants to know that the broker genuinely did approach as many underwriters as they claim and validate that the underwriters did reply with the quotes that the broker claims were replied. (This is how the client makes sure that the broker and the underwriter aren't colluding.)
The end result is that across the industry there is a many-to-many broadcast and scatter and gather that needs to happen and be notarised. (The broker sending stuff out, the underwriters responding.)
At the moment, there is usually a third party hub through which these documents flow who essentially notarises the communications, but also has no incentive to allow collusion between parties. So everyone trusts that third party.
The only problem is, there is no incentive for the third party to be efficient, and so in every country / state / market where this kind of system operates, the third party inevitably takes a large cut of fees and provides quite remarkably terrible service. (Case in point: "of course it's secure, it's on port 443". "Umm, you are actually just making an HTTP connection on port 443, there's no SSL happening on this connection, as can be seen in this packet trace.")
The brokers hate how it has played out, the underwriters hate it even more. With a bit of handwaving, this is something that can be solved by a blockchain. Although the unencrypted documents themselves probably can't be on the blockchain, the checksums can be, and maybe there's a scheme where the encrypted versions of documents can be there too.
It's one of those situations that blockchains are good for: distributed system, no trust required, the users of the blockchain can afford the appropriate technical skills to keep the system running, can't be replaced by an independent 3rd party, etc. etc.
But it's not likely to happen.
The main problem is that there's no monetary incentive for any individual party to build the system. It's a tragedy of the commons problem: once it is in place, it will get used, but no-one wants to pay for it because if someone else can pay for it first then that's a better arrangement.
So yeah, five years of discussions and learning about the market, and everyone wants it to exist but no-one wants to pay.