It's not about it being impossible to cryptographically prove/validate it, but rather about services choosing to not attempt to try to validate it. They generally don't provide such an option, because it's tricky, somewhat manual, has certain costs and risks, and no benefit to the service provider.
If some law prescribes that after following a certain verification process, the operator is required to delete the account, then that legally mandated process would work, but in the absence of such a law literally no process can be sufficient, because the operators can and will choose to ignore it, no matter how reliable it is.
If I prepare for it, sure. At that point, I can just leave my password though. I was responding to the point that you don’t need to leave the password because a death certificate would be enough.
But maybe I don't want to leave my password behind because I'm weird that way or something, and instead I just want my account nuked.
Cryptographic proof of ownership by the dead guy + death certificate should allow for account nuking, without allowing for a third party to do something else with my account.
(Not that I'm worried about it, myself. In fact, I've found all of these dead man's switch/after-death automations pretty amusing every time I've seen them pop up in the past couple of decades.
I mean: When I'm dead, my HN/Google/whatever accounts will become idle, and I'm dead AF so I don't care if someone hacks the passwords some time later. It's a non-refundable one-way ticket for me.)
Leave a public key in your HN bio.
And leave a matching private key and validation instructions in your will.
If the keys match along with a death certificate, then: The account owner is validated as being dead.