Actually the Stonewall “Attack” (chess) ♟️ is quite symmetrical. And the Caro-Kann. The Botvinnick Attack is an attempt to break symmetry.
The QGD is also quite symmetrical, often stretched out into long endgames.
Just a few to name
(USCF high 2033)
White moves first. That’s a significant asymmetry, is it not?