The problem with BRD/MCH auto attack is that it's affected by a range penalty (as well as any other attack without GB/WM active), on top of their relatively low weapon damage to begin with. It's only been until now that their damage had some what resembelence of consistency, where beforehand GB/WM had the same ranged damage penalty and it'd fluctuate wildly between a 0% and 75%+ damage reduction because they were too far or too close (and they had to address that for seal rock due to GB/WM eliminating your free mobility) With the interrupt changes, there's very little advantage to having GB/WM off when even feint can do more damage on a typical basis (no range penalty), exception being to set up BRD DoTs and MCH procs. There's other things to consider when your target on the move (they aren't casting, for one). And you can also set weapon skills to auto-face target. Or if you're playing standard, you'd keep them within your range anyway with right click.
And since you want to bring up damage dealt (because as I mentioned before, you can't take this for direct context) tell me how you lost when you have less overall deaths. Maybe your tank died with 300 medals at the very end due 9 stacks of heavy medal. There's another factor on healers who focus on preventing damage rather than healing it back up. It's certainly not being overwhelmed.
I'll bring this up again, would you rather send a melee such as a DRG or MNK to harass/interrupt a spell caster like a BLM, or a MCH/BRD?