Trustless: episode 4 -- trustless society?

We've established that the Bitcoin network is trustless in some sense. We still trust in some aspects of it, but typically we don't have to place our full trust in an intermediary, like we do with our bank.

One question is, should we attempt to bring some of these ideas into society? Should we strive for designing society in such a way that trust in an intermediary is not required? (I am speaking hypothetically, not knowing whether such a thing is technically feasible.)

For example, I tend to trust my doctor. I believe that he cares for my health. If it was possible for me not to have to trust him, would I like that?

I don't know if I would.

It is not easy to put into words, but I see value in the fact that the doctor believes that it is his responsibility to help me conserve my health. And I see value in the fact that this belief comes unbidden, not from an outside constraint. If the system was trustless, the doctor may be less passionate and dedicated to his mission, and we could both lose value: he would feel diminished in his practice, and I may get less devoted treatment as a result.

What do you think? Should society be trustless?

Check out the next episode, on trustless politics!