Two comments
When I first read the rule for primary scoring, I was unclear whether it compared the quantity of cards or the ranks of cards. But it's just the quantity of cards, right?
So it seems like card ranks only matter for the tiebreaker, which (as you note) doesn't really extend the strategic space of the game. Are ties common enough that there even needs to be a tiebreaker? If there does, you could just say that if there is a tie on points then the winner is the player who won the top-most Ace. If there was a tie on that Ace, then the player who won the second-highest Ace. And so on.