There are all sorts of uses for cryptographic proofs; e.g. you can sign a document and prove that you were the one who signed it, or you can do a bunch of double-SHA hashes and prove ownership of a Bitcoin, you can prove via a SSL certificate that the content that claims to come from somedomain.example actually does, etc etc.

But there's no way, via currently existing protocols, to deliver a document with a proof that the document does not contain code designed to track the user or that the document will display properly without running arbitrary scripts.

Gemini is bikeshedding, yes. But it solves this social problem - a problem of expectations. You can't make a webpage with tracking scripts and deliver it over Gemeni because there's no point. No one who received the document would actually execute any of the scripts. So Gemini succeeds at creating a little insular community where tracking and web analytics are not just forbidden, but impossible.