The only real AoE that cannot be avoided or reduced is Tank Purge. Often times when healing is intense it's because people are getting hit by eruptions and Ifrit, getting hit by lasers, or suiciding into linked orbs. As for tanks, many of them I see not avoiding lasers, plumes, Ifrit, or end up standing in the wrong spot when bombs drop. Then comes Deflector Beam and they don't even have enough health to survive it.

I find it helps to designate one person to the tanks and one for the rest of the raid. I usually stay close to the front so I'm never too far away from tanks; the white mage and Eos can handle the raid healing. Some tanks also tend to wait for too many stacks of the debuff before swapping, when it's perfecting doable at 3 stacks or even 2.