At least in my country, storing money in a bank is mainly trustworthy because of the Federal Deposit Insurance Corporation under which deposits to accredited banks are ensured by the USGovt even if the bank fails. Before the FDIC, putting money under a mattress was a reasonable solution. Longer term people would buy precious metal or whatever. I just cant get on board with you that in the future, taking responsibility for yourself will be outdated.
But don't you want the whole money chain to be trustless? That's what I think we will have in the future. Instead of banks or mattresses the money will be stored on a distributed block chain. And instead of managing private keys, there will be a global user ID system that will keep the money safe and connected to individuals anonymously.
I could be wrong. Such user ID system is easier said than done. Biometrics can be shaky and counterfeit. ID cards can be stolen. Tricky problem.
We will see. Maybe you are right! That there will always be necessary to manage the security of private property oneself or having to trust a third party.
I think I finally understand where you are coming from on this. However, I thing that the kind of "trustlessness" that you're talking about isn't really trustless, it's just trusting in a community. Indeed, I think this is a powerful idea. And you might be right about some eventual implementation, I'm not convinced though. Anyway, I'm glad I finally understand what kind of thing you're referring to.