Howland Reed is still out there somewhere, staying mysteriously out of the fray. And who were those two handmaidens in the room with Lyanna? Could one of them resurface? Does Littlefinger know the truth about Jon's parentage? That conversation he had with Sansa in season five seemed to imply that he knew Rhaegar loved Lyanna.

Having a witness come forward to support Jon's parentage would help people believe that Jon's not Ned's bastard son and is half Targaryen.

It's important that someone other than Bran knows the truth. Imagine Bran trying to convince people by explaining that he's the Three Eyed Raven and can see past events in Westeros. They might think he's crazy.