My theory is that Shakespeare is full of old jokes and old metaphors, for which we don't have an earlier written version. He is this one person that is so often quoted and repeated that it seems unbelievable that he could come up with so many memorable lines. It may be that he was the person who made the works of art that preserved the cliches of his era.
It's a good bet that a new phrase which would require explanation is not something you're likely to put in a play. But most of the stuff that Shakespeare scholars credit to him probably did originate with him.
The printing press was well established in Europe by his time (to preserve any prior art), and Shakespeare had an astounding gift for language.
