Can cryptography change the state of affairs in this regard?

The whole problem is reputation management here. From eBay's perspective, they did not have strong enough signals that you are an honest person.

With cryptography, you could sign something like "It's me, Joe So And So - signed by the owner of joesoandso.eth". "Oh and here are cryptographically signed endorsements of 3 of my friends who are long term users of eBay". So that eBay has strong evidence you are a reputable person. In an automatable fashion.