we said: "No, because there is also technology that makes it possible to trust anything electronic with very nearly 100% reliability. But no one uses it"
I think your first statement is both technically wrong and generally wrong. Electronic trust is a solved problem...it's just that right now, it's really not as big a deal as some people are worried about it being, so we haven't generally implemented the solution. We could make electronic cars for long time before other things made them commercially viable.
I disagree that electronic trust is a solved problem. It is mathematically solved, yes, but the reason that it isn't widely used is because it's still intrusive and painful to do. A solution that isn't acceptable to the masses isn't an effective solution.
If it could be done in a way that is invisible (like HTTPS, for instance), then it would be ubiquitous. That's the part of the problem space that still needs resolution.
I send you a bunch of bytes signed with my private key (which somehow you have to verify in a trusted way) and you can be sure that I am the person who signed those bytes (unless I was compromised).
USB etc hardware keys can be used protect accounts like Gmail, Coinbase, web hosting services, many more now.
Fun fact: it's possible to receive Facebook user notification emails encrypted against your public PGP key.