In the end it doesnt matter how much stuff you get hit by as a dps, as long as the raid ends the fight alive and you did enough dps to kill the boss.
Good example is protectors heroic. A joke of a boss which we one shotted each week. This week we had 2 new trial healers who wern't really pulling their weight and people were ticking down from garrots to about 50% of their hp all the time makes the fight quite a bit more tricky as a dps. Suddenly you need to pay attention to Sha Sear and use a cooldown if you're targetted. Suddenly you get one shotted by poison pools while you only run over them, and not stand in them, taking one tick only. Suddenly a single tick of Rook's whirlwind kills you. Now if the kills were so smooth when you had your usual healer setup, and suddenly get troublesome when you switch 2 healers around, you can blame this on the dps taking too much random damage, but the healers surely are part of the problem aswell then.
A healer is not only there to outheal unavoidable damage, a good healer is also capable of recovering a situation where a dps messes up. Its the team effort that matters in the end. When a healer is at full mana and 1 person in the raid is standing in some bad shit that healer should go ahead and heal him. If this healer doesnt react fast and lets that person die while he could have saved that person the healer failed on his job aswell in my eyes.
On farm people tend to slack slightly on moving out of stuff. Now you can choose to make your life hard and remove healers on farm (so that dps is still forced to dodge every single thing), or you can just slightly overheal fights so you can faceroll your way over them. I prefer the last. And a good healer setup makes your whole progression smoother in a similar way.