This has been said to a certain degree, but it is worth saying again: healing isn’t stressful, healing bad DPSers and tanks is stressful. The difference between a smooth run and one where the mechanics aren’t being done is incredible. The amount of avoidable damage that often isn’t avoided is incredible. When a mechanic is missed, occasionally a healer can save everyone. When they can’t, most likely the people who missed the mechanic have no idea they messed up, and all they notice is the wipe. Which they blame on the healer.
You can say that Bliz made healing harder, or you can say that Bliz made it more important to actually do the mechanics, because the healer probably can’t save you. It’s worth noting that very good teams can go without a healer; that shouldn’t tell you that a healers who can’t keep everyone alive are bad, but that DPSers who die EVEN WITH a healer pumping are missing something profoundly.