If they know all your accounts, passwords, PINs, etc, that's one thing - though you have to trust that, if and when the business dies, they properly wipe their hard drives.
But if they have your digital life (all of it), and they go under, then all your data is gone. So: Your approach of having them have your passwords and PINs is better than "one stop shopping" where they alone hold all your data.
I would think that the way it would work is that you when you sign up for the service you create a master document with accounts and passwords that gets encrypted before it's uploaded to their servers. Then, in the event if a catastrophe, you just send them your encryption key for that profile and they do their thing and reset all of your accounts.
It might work. Chrome already saves all your passwords on Google's servers (if you allow it too) and Apple does the same with Keychain on iCloud. So it's definitely going there, and if you can get users to trust your service, it might take off.
Think of it like an emergency service for your digital life (both private and business).
I suppose you could put it in a safe deposit box. Another option is hide it in the margin of a book; somewhere that normally wouldn't get stolen or read. Of course then you have to worry about fires and floods... Perhaps a copy at a relatives house as well as yours. For bonus points, don't tell the relative, just jot it down in a book on a shelf when he/she isn't looking!
It was largely rhetorical. :P A lot of the comments on this are related to how do you keep important data both always available to you, -and- safe from anyone else getting ahold of it. I was just pointing out the bootstrapping issue; having one password/phrase/key that allows you to reset the passwords/whatever to your digital life still requires you to find a way to keep that one word/phrase/key safe yet accessible.
But if they have your digital life (all of it), and they go under, then all your data is gone. So: Your approach of having them have your passwords and PINs is better than "one stop shopping" where they alone hold all your data.