From the tone of your statement, I think you meant mis-understanding. I'll add also a misunderstanding of macroeconomics and a rejection of empiricism. The cryptocurrency folks read a bit too much of von Mises.
I'd say, you can (Bitcoin is one of many recent exercises of replacing trust with math). But it's not worth the price. Or, put another way, trust is a ridiculously powerful optimization that enabled humanity to form societies in the first place. It's very similar to how introducing a central node into a network reduces communication costs from O(n^2) to O(n). In the general case, it's stupid to not take advantage of it.
I consider Bitcoin to be the closest we've came so far to expressing trust in units of energy. POW shows us how much computation has to happen to achieve mathematical guarantees in lieu of trust. Somebody could probably derive some upper and lower bounds on the energy costs of trust in terms of information theory. I'd love to read such a paper.
Even in the very basic ecommerce use case: buyer purchases item online with bitcoin. The buyer must necessarily trust the vendor to deliver.
There's no recourse outside of the good graces of the vendor. There's no chargebacks or third party mediation.
Thus Bitcoin actually reverses the risk assumed by online purchases from the vendor to the buyer.
This is the reason why Bitcoin is a failure outside of niche grey and black market concerns. It is far worse for the consumer than existing solutions that isolate them from transaction risk, and will usually kick back a small percentage in cash back.
So much talk about the benefit of crypto currencies seems - in my eyes at least - based on a fundamental misunderstanding of how societies work.
And most of all: you can’t replace trust with tech.