In three plies (one sided moves) of chess, there are over eight thousand possible games. By making the game 960 times as wide before you start you're not meaningfully changing the impact of memorization on the outcome of the game. You're just changing how deep you memorize the various trees.

You can say, "well then, mission accomplished!" but the reality is that most of the tree memorization goes pretty deep at the highest levels before a new game is found because you're in effect following the games before it or you're blundering, or, at best, gambling if you've found something kinda unexpected and interesting.

Put another way, any given top rated chess player has a finite set of possible game memorizations. Introducing a mere 960 new configurations at move 0 is only trading 2 to 4 plies worth of depth to the game. It's more complicated than that, because board positions can be essentially forced and board positions can overlap between pre-configurations, etc. But that's the essence of my argument.

You're not meaningfully changing the impact of memorization on the outcome of the game, even if one thousandth sounds like a lot, it isn't really when dealing with permutations.