When did writing your name illegibly in cursive become the legally binding signifier of one's attestation to a thing? The signature could have been anything, so long as we all agreed to it and it was forensically associable to you.
I like to imagine a universe in which the signature was instead a little drop of blood dripped onto the signature line. In that world, you'd leaf through the pages of your lease agreement, arrive at the signature page, check your pockets, turn to the agent, slightly embarrassed, and say, "Sorry, do you have a pin I could borrow?"