There is one big problem with this proposed rule change. What if, as is often the case, both players are playing for a win, in their own personal styles, but neither succeeds? One of the players is unjustly penalised.
Is it being suggested that players in classical games should play more recklessly, illogically or not in their personal style, and that a win counts for more than the quality of the game? That’s what blitz and rapid are for.
To reduce the number of draws I suggest adjusting the points score for draws.
The new score would be .3 instead of .5 for the higher rated player and the rating deduction would be adjusted accordingly. It doesn't seem possible to change the rules of the game to the general approval and adjusting the scoring should be done with the smallest change possible needed to achieve the desired result.
Giving extra points for a win only provides an incentive for future draws as does giving extra points to a lower rated player achieving a draw. This would hopefully have the twofold benefit of forcing the higher rated player to be more enterprising and reduce the rating inflation inherent in the current system.
This should not lead to more draws because the lower rated player is trying to draw as it would be offset by his opponent trying harder to win.
It might be one of the ways to effect the least change in the rules while only penalizing draws.
This idea might also be beneficial to other sports where draws are a problem.