I don't know all the mathematics, but I do know what you describe gives an advantage to the house.
Another thing I've seen popping up is Blackjack using a video screen to show your cards instead of real, physical playing cards. Now THAT would be impossible to beat as I'm guessing a new "deck of cards" is used for every deal.
There was another twist to the blackjack they had on a cruise ship I was on last year. All cards were dealt face up, including the two dealer cards. It made it really easy to decide whether to hit or stand. The kicker? The dealer won all ties. I didn't play it for very long, but I lost during the little time I did play. When I got back home, I did some research and learned that version of Blackjack gave the house a decided advantage and, even if you were a counter, was a losing proposition.