I think you're using the concept of "trust minimization" too loosely. Bitcoin does not try to create a world where people cannot trust each other. Bitcoin aims to design a monetary system that is robust against untrustworthy actors, which we all know exist.

Bitcoiners like the phrase "Bitcoin is trustless". But a better way to say this might be that Bitcoin is "game-theoretically secure". Bitcoin is a system that can work and produce socially desirable outcomes without requiring that the agents place trust in a small coalition of actors.

By contrast, fiat money requires the mass of agents to trust a subset of agents to act in a certain way. If the "trusted agents" do not act in the prescribed manner, then it leads to undesirable outcomes. If the mass of agents no longer trust the subset, then the entire system fails. Fiat is therefore not game-theoretically secure or robust.