Strangers require globally verifiable proof of work to obtain trust.
Once that hurdle is cleared, locally verifiable proof of work can suffice. This is trust.
Discussion
Proof of work does not create trust.
It is a mechanism that reduces an infinite amount of states into 1 “best” one. That is it.
Proof of work in this context is something like a ball always falling to the ground when you drop it. Physical proof of gravity's force applied to the ball.
Once you've verified that things drop when you let go of them, you don't have to verify it every time. You can trust gravity to work in the future as it worked in the past.
Someone can prove they have a good character, but they could be deceiving you. Securing trust between people is harder than securing trust with physics. So you need them to occasionally exert some force in the real world in your benefit to maintain trust.
Trust is formed from leverage and/or cost. In the end: breaking it will permanently cause significant loss.
The problem is proof of work is not a real cost. Anyone can buy it, while you can’t buy real social relations. And once it’s over, your identity is trashed forever.
Proof of work is also a sunk cost, so whether you break the so called “trust” or you don’t, it’s gone.