The group is losing a ton of overall damage by adding a Red Mage over a 2x Minuet Bard. The difference in healing is negligible since neither party is going to have deaths if they are even half good.

You're looking at adding in one Red Mage's damage (who is not getting attack buffs btw, Marches/Haste only) as opposed to adding 2x Minuets to 3 Heavy DDs.

Would the "sky fall"? Subjective. Is the exchange anywhere near equivalent? No, it really isn't. Think of it this way. What would have happened if a THF replaced that minuetBRD? Exactly. And Thf is a stronger DD than Rdm to boot.

That's not even getting into the business of Corsair, which was significantly better in that slot than both Bard and Red Mage combined. Corsair is a stronger DD than Red Mage, and can give a buff comparable to Minuet while also boosting EXP and giving the mage a second Refresh.