Indeed. 308s probably don't need any reinforcement in this area as they have tube (space) frames.That is a major piece of bracing, clearly much heavier than is what's needed to just support a center console. I would leave it in place, even racing Xs have it in place. You are customizing an X, not recreating a 308 so a little diversion is just fine. You climb into an X and wear it like a worn pair if jeans, a spider you jump into like hopping onto your favorite couch.
Having spouted all that, I'm willing to bet that in normal day to day street driving you wouldn't notice the brace missing but who wants to take the chance.