There's an argument that Shakespeare didn't coin (all or some of) those phrases or words, that they were in common everyday use at the time but never written do

There's an argument that Shakespeare didn't coin (all or some of) those phrases or words, that they were in common everyday use at the time but never written down because the type of people who used them couldn't write. That would still be valuable in disseminating those neologisms further and giving them staying power, but it's less discovery and more documenting.