I think you're missing the point. You're thinking about it from a magician's point of view. Think about the effect as a whole. The effect is that you spell to their card. Why does this card need to be signed? To prove that that was their card? Not really. As long as you show that you don't have a forcing deck, there's really no point plot-wise of signing the thing, I'd have to agree with Alex. It's not like an ACR where it makes sense for the card to be signed. You said yourself that the main point isn't that they will be sure it's their card. The main point is cleaning up for the sake of cleaning up, which makes it unnecessary. Of course if you want to end clean then that's your personal preference, but it's a bit like using a complex sleight instead of a simple one because you want to show off your skill to other magicians.
Also, although I don't have Psypher per se (I bought the original UI and am very familiar with many different types of similar devices in general), I'm not sure what the point of cleaning up in this situation is. I know what Psypher is and how it works - but if there's suspicion on the gimmick, given what the effect is, then the performer has done something terribly, terribly wrong and cleaning up should be the least of their concerns.