you can just write a doc with your proof/idea, hash it and post that hash on twitter

Not so easy. The problem is that someone can "just" generate a lot of documents with different or contradicting predictions or idea and then selectively release some.

Yes, you can. So maybe we'll see an adoption of that paradigm, or another. The value of a ZKP is that you can optionally prove some facts up front about the file, whereas a normal hash is all-or-nothing. You can't reveal part of the information because you need the entire contents to properly verify the hash.