Practically speaking, couldn't I just tweet the SHA1 hash and let Twitter be my trusted timestamp authority? Assuming I don't work for Twitter, it's unlikely I'm able to modify the timestamp on a tweet. (The blockchain has a lot more confidence due to its distributed nature, but in the minds of say, a jury of your peers, I bet it actually appears shadier than Twitter.)
Yes, but that would be a centralized solution. When Twitter dies (wont happen, but still) or a rogue admin changes the timestamp, etc. - It requires a trusted party - Twitter - instead of the blockchain.