Trust is the willingness to be vulnerable to the actions of another party based on the expectation that the other will perform a particular action important to the person doing the trusting. This is regardless of whether the person can monitor or control the party they are trusting. Trust is a quality and mechanism of human relations, of being social.
There is no need to trust that 2+2 will equal 4 tomorrow, it just will. Ditto other deterministic processes such as cryptography.
Distributed ledgers bypass the immediate need for trust. Trust is relocated and concentrated in those elite groups that do the protocol designing and coding. We must trust that they know their stuff.
The wider interactions that previously involved trust, indeed nurtured it, have no further need for it. Quite possibly, the absence of trustless proof may engender distrust.