The easiest way to illustrate this is with openings, though it applies throughout the game in different ways. Against e4 the Najdorf defense was once the opening of champions, being a major part of the repertoire of players like Kasparov and Fischer. In modern times it's an increasingly rare guest at the highest level. It's not because it's considered unsound or even slightly dubious - it's a rock solid opening that gives black real winning chances. But the problem is it also gives him real losing chances. It's complex, difficult to play, and if you get outprepared by your opponent you may lose without him even having to make a single move himself, which is really one of the worst feelings in the world.
So instead the meta has largely shifted to openings that are more about minimizing risk where black, more or less, aims for a draw - and usually gets it. Changing the risk:reward ratios in a sufficiently extreme way is most certainly capable of changing the meta.
I am not good at chess but would it help if win as black was rewarded more than win as white?
One tie break system, armageddon, does break the symmetry by giving black draw odds (he wins if the game is drawn) but less time in a blitz game. But it's very poorly regarded and generally only used as a this-game-MUST-have-a-decisive-result last resort.