I'd probably pay a small amount for that, assuming that the security features were incredible.
Some of the issues I've considered:
1) Giving a password to someone is a major security hole. They could lose it, it could be stolen, etc. This is going to be a key to your entire (ideally) online presence. And for people with online wealth this poses a significant issue.
2) This sort of system requires updating and ideally you'd want to make it as simple as possible.
3) What if not all of your digital assets are online website accounts. What about MMOs? Or FTPs etc. Online banking.
4) The digital information security as you mentioned will of course be a large priority.
5) What if a client doesn't have someone to give their information to? Then it would / could fall on us to be aware of his death. I haven't found a good way to do this other than a rather morbid dead-man switch. Call them at some frequency just to check up on them...
My option is to save all my necessary login informations, encrypt it, and leave in my will for the executor/trix to handle and act out my instructions.
This topic is one I've pondered as a basis for a startup but I have yet to find a really significant business plan surrounding it.