I agree that signatures on the synthetic covers is a bad idea and they sell for a deep discount.
That said, I will share some of my experience to the contrary.
Back before I knew better, I got a bunch of signatures on Rawlings Official League baseballs with a synthetic cover. Twenty years later most of them bled and the signatures look horrible. I have feathered rookie Jeters I can use for tossing in the yard.
BUT, for whatever reason, some of them held the signature perfectly with no bleeding and the balls are still snow white. They look and display great.
I guess it depends on how the ink from certain pens interacts with the synthetic cover.