The biggest problem with this is what happens if one of those people dies - or simply gets a new email and doesn't tell you - before you die?
Your data is forever locked because of one person. It's even worse than you not telling the service that you changed your email. At least you should have known that the service existed.
Burdening your friends and relatives doesn't strike me as the best way t handle this issue.
1 person has responded - the person who clicked the button. If nobody else agrees, then I would say the data stays locked. Otherwise the one person could simply wait for a moment where everyone traveled and had no email access.
Which basically means to say that the entire security of the site is based on the ability of my designates to have my best interests at heart... and also not to have installed a spam filter, moved, changed email or otherwise become unreachable to a service that pretty much becomes forgettable after 6 months or so.
I'd much rather trust myself to manage things, to be honest.
Your data is forever locked because of one person. It's even worse than you not telling the service that you changed your email. At least you should have known that the service existed.
Burdening your friends and relatives doesn't strike me as the best way t handle this issue.