Before I answer that, I want to point something about about DPS checks, healers, and healing responsibilities. The only fights that have DPS checks are EX content and beyond. Everything else doesn't have a DPS check, so it doesn't matter if you were to theoretically get overwhelmed healing because the boss isn't going to do anything with this extra time it's taking to clear a fight.
As for EX content and beyond, the experience of running these forms of content has 3 distinct phases: prog, first clear, and reclears. While in prog, your DPS doesn't matter unless you have some type of mini DPS check like the flames or add phase of P3S, but that's not super common in this game, and I'll return to this in a moment. Beyond that, whether or not anyone in the party is DPSing is irrelevant, because your goal is to see and learn mechanics. Only after you get through those mechanics does DPS begin to matter. Once you reach that point, your party isn't making mistakes often enough for that to be an issue, and if they are, you're not hitting the DPS check anyway. Also, a party mess up is something that doesn't take long to recover from. In savage and ultimate, healers are still in the 80%+ range of time spent DPSing. Once you get to reclears, this process only refines itself more and more.
Additionally, the bulk of healing resources are designed innately to not interfere with your DPS. The vast majority of healing healers will use is OGCD. What DPS spells is that interrupting? Or you have the lily system on WHM, which not only refunds your lost damage, but can also be optimized to increase WHM's damage output.
As for mini DPS checks, the system we have already handles this quite well. Doing P3S as SGE, I never had to drop attacking birds because I had OGCDs, and I could cast an E. Prognosis between phases when there were no targets. Every healer can manage this quite fairly. Whether it's having OGCDs, or having GCD heals that refund your DPS, healers have the tools necessary to get through these phases, and even if you are struggling, isn't the point of savage to be difficult and to ask players to improve and polish their performance?
Ultimately though, this comment has been brought up many times before, and I want to ask, where does it honestly apply? Because as someone who does content that has DPS checks, I do not see where this is a problem. I don't see it now in tier 2 savage either where I'm playing as a DNC, and the healing is left up to my teammates instead of me. So I'd really like to know why people think this is a problem that's going to prevent players from clearing content. The biggest group of people it affects are week 1 raiders who are at the cream of the crop for their roles generally. Those healers are not playing as poorly as the casual healer who would struggle in that environment, but casual healers don't go to that environment to begin with. What's the issue?