Cue an ad for BIP38 (Password-Protected Paper Wallets).
If I were to create password-protected paper wallets, and put copies in two separate safety deposit boxes at two different banks, and then memorize the passphrase as well as share it with one or two trusted individuals, that's a whole lot better than shoving cash under the mattress.
Point conceded, good sir. But that's quite a bit of extra work and you're still putting trust in other individuals. Not to mention the cost of the safety deposit boxes which, on an annual basis could (I'm not saying they would, but they
could) exceed the cost of the insurance itself.
Would it not be beneficial in some people's eyes to have the easier access, with less hassle, of the insurance based model than the paper wallet model? As I'm sure there are plenty of people that would not divorce themselves from their paper wallets, and others who would never bring themselves to adopt them.
You could argue that the extra risk associated with trusting a third party insurer creates an extra "risk cost" as opposed to your trusted individuals, but the different costs and risks associated may very well balance each other out to be rather equal in the end, assuming that an extremely trustworthy insurance entity came to be.
Then my argument would shift to the idea that having the client-insurance based model would lead to more opportunities for extra utility as opposed to the paper wallet.