It can drastically throw off bounded accuracy. It's one of the few switches and knobs in this game that, if you throw it carelessly, you may be throwing things well off balance. If you given them a +2 to hit, you're giving them the equivalent of a high level very rare magic weapon. I think in your mind, you're still working off the concepts learned through years of 3e/4e. +2 is not a "smaller" circumstance modifier. It's often a HUGE modifier. People keep trying to translate advantage into a +X to hit, but it's really not the same thing. The +X alters the target you are capable of hitting. The Advantage only alters the luck of the die, not the target you're capable of hitting. It's a meaningful difference.
I really don't see how occasionally awarding 'The DM's Best Friend', a +2 bonus for 'favorable circumstances', or a -2 penalty for 'unfavorable circumstances', could have such this destructive game-warping effect you describe.
And what is your take on Half Cover, which grants such a +2 bonus, and is already a part of the game rules?