This is an inappropriate analogy. Chess at the highest levels is not drawish because the game is inherently drawish but because the meta of it is.
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.
The current trend has to been to increase the value of any win, with things like 3 points for a win and only 1 point for a draw. In my opinion increasing the points based on color is an interesting idea, but it's unlikely to be seriously considered because of the fact that it would disrupt the "symmetry" in chess both the sort of abstract fashion, and also in the specific - such as requiring tournament pairing systems based on score to be completely reworked.
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.
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.