You could sign it forward. Slightly harder to validate, but maybe if the original PDF included your key - that should maintain a clear chain of custody on the PDF itself.
Oh for sure. And the existence of the signed on copy with a timestamp can invalidate later signed copies, etc.
This is just a mechanism that provides that in a general way.
It’s sort of like, how, before Uber you could call up the few cabbies you had who you liked and get a ride but having Uber was a game changer anyway because the friction fell below some threshold.