The difference between a digital signature and a timestamp is the timestamp. It's not just that you had the document. It's that you had the document at a specific time.
I don't know what you mean by "you had the document", but if you mean "you've last modified it at x": yeah, a digital signature automatically does that. It tells you, in a forgery-proof way, what person modified a document and when. If someone tries to manipulate the document, the signature gets broken.
If you mean "who has last opened it": you're describing a DRM. Also been a thing for two decades.