I completely agree with this.
Where possible I prefer to bump damage dice up (dice shift), rather than give static bonuses for the reasons given. Using "dice shifts" in-game though can be cumbersome so I don't mind that a PC strength bonus does +1 to +3 damage. Afterall players often switch weapons during the game or suffer changes to their abilities and I don't want to be figuring these things out everytime someone changes their weapon.
For an NPC though, that you will likely have generated before the game begins, you can do the mental math and dice shift then though. I suppose the ogre might pick up a different weapon during the game but you do your best to find the right die or use an appropriate + then, on the fly.
I'm good with the die shifts. But I prefer bholmes' approach. I don't mind the +1 or +3 to damage either. I mean, imagine if you have a Thief with a dagger and a -2 STR modifier. Mkay, so you can get it figured that the -2 will drop the dagger to a 1d2 damage. Yikes. But then he picks up a short sword... at some point all the die shifting up and down reaches a critical mass.
I like the idea of shifting dice up and down too. But I don't want to go overboard with it. "+2DS because opponent is blinded, +1DS because an opponent is flanked, -1DS because of STR modifier" isn't any better than applying modifiers to a die roll.
I'd rather not apply the die shifts for everything. Using it to represent a weapon that does more (or less) damage? I'm cool with that. Using it instead of ability modifiers? I'm not cool with that.