The way I see it, is that you're creating another conviction, one that the deck is truly mixed face up and face down. The triumph plot has two climaxes, the first being that the deck is straightened out and of course the second one is that the selected card has been found.
When both climaxes are realized at the same time, the impact it produces is somewhat less than what it could be.
You can do a triumph effect without a selected card, one of simply shuffling face up cards into face down, and showing the deck to be sorted, and still have a tremendous impact. Why subtract from that climax by mixing it with the revelation of the selection?
That's just my view, and in my experience and with my presentation style, the way I suggested works much better for me, and seems to have a greater impact on my spectators.