Instead, why not use the blockchain and crypto to prove that someone wrote about an assault when it happened, not years later?

You could write a hash of what happened to you to the blockchain. It can't be removed. It will stay forever. The beauty of it is that you can make the name of the perpetrator public, but the content of the accusation secret (hashed). The benefit is that other victims can find each other and compare notes, while the accused can't access the accusation and can't sue for libel and silence you.

If, years later, that particular person (Bob to abuse crypto conventions) is selected for the supreme court, Alice can reveal the source of the hash, therefore proving that the allegation was documented at the time the incident happened.

All it would take is a simple website where victims would write down what happened to them. Then post on the blockchain, let the user archive, and that's it. There are a bunch of challenges (cost, spam) that would need to be investigated further of course.

[1] https://www.washingtonpost.com/outlook/i-reported-my-rapist-today-so-he-cant-become-a-supreme-court-justice-later/2018/10/04/09d7bf10-c74d-11e8-b1ed-1d2d65b86d0c_story.html