yes, and there are 2 other major reasons the player will have an edge and one minor reason
the player is more likely to catch a winning 10 or Ace or 9 on his double downs
and the player is not required to hit when he has hard 12, 13, 14, 15 or 16 but the dealer is - since there are more high cards than low cards left he will bust more often than when there aren't more high cards left
and the minor reason is that the player is better off on his splits for various reasons but not by a great amount