Sure, but that doesn't mean you assume that the user operates their own bank. They have some third party they trust to hold their money for them. There are risks to that, but in practice it turns out those risks are much less grave than the risks associated with everybody holding their life savings under their mattress.

This is why I've always been skeptical of the "everyone should have their own server" vision: servers require administration, administration requires technical skills that most people will never have, and even lots of those that do have them aren't necessarily skilled enough to be able to keep them reliable and secure. For all those people, having some professionals at a third party deal with that stuff will yield better results than DIY will. There are risks here too, but it'll probably be easier to mitigate them via regulation than it would be to teach everyone in the world to speak Unix.

(The one way out of this trap would be if we could come up with some kind of server that did not require administration -- that had guaranteed 100% uptime, that never required security updates, that scaled automatically to meet any level of demand, that didn't have physical parts that wear out over time, etc. It's telling that the closest thing we have to that today is less a server and more something like AWS, which... requires trusting a third party.)