You're confusing strategizing a game with memorizing it. That you can break the system isn't a valid reason for prohibiting people who want to from playing it for real. If played correctly, there should be no difference in your chances the first time you encounter an unfamiliar NPC from the 100th time you repeat the same match with him (other than by upgrading your own deck or your skill in the meantime). Currently, the prevailing approach (because it's the only one the time limits allow), is essentially to cheat, manipulating the game based off memorizing the software's pattern logic. We should be allowed to instead choose moves based on the strategy of the Triple Triad game itself and its assorted rules.
You sort of started arguing against your own point there, but anyway... Chess pieces are far simpler and more straightforward. In chess, a knight is always a knight and always moves the way a knight does. A rook is always a rook and always moves the way a rook does. Furthermore, you always know that each player will have exactly two of each of them. The rules are fixed and unchanging, and so are the pieces. In TT, the way a given card "moves" (which in this case means what effect it has) varies according to which rules are applied to the game.
The only thing making Triple Triad easier to master than chess is the fact that TT games are so short. With only nine moves in the entire game, you never have to plan more than seven or eight moves ahead, and by midgame, that's down to four. But that's still a lot of possibilities to consider, especially if some of those possibilities trigger combos that change the makeup of the whole board. With 30 seconds, you don't get to consider any of them.