WHM doesn't also have to worry about using that oGCD heal that could potentially lock them out of using their oGCD AoE heal, oGCD AoE DPS (more specifically their DoT spreader), oGCD damage/MP restorer, and oGCD tank-buster heal since they would lack the resource to do it (except for maybe Divine Benison) or sacrificing a whole different set of cooldowns and their passive heal to get the resources to do it.
On top of that, all healers, not just the SCH, want to avoid using their GCD heals as much as possible, but SCH wants to avoid them even harder than the other two since those heals are weak and expensive. When it comes down to using their GCD heals, the WHM and AST can do it better and more efficiently than the SCH to go back to DPSing sooner. SCH usually has to leave it to someone else because they pretty much can't. As soon as the bulk of the healing falls on the SCH, unless they're overgeared or have all of their cooldowns available, the SCH will struggle much more than the other two. That's not good balance. The problem of not being able to heal content was exactly why AST was initially barred from content. True, it's not so bad that SCH can't physically heal anything, but it's come to a point where you have to ask "What does SCH bring that the other two can't do?" Yeah, they have good oGCD heals, but Earthly Star is godly when timed right, and WHM has Assize, Medica, Cure III, and PI. SCH has Indom... on a 30s timer. SCH has Succor... that's a weak heal and weak shields and not much better under Emergency Tactics that's on a 20s cooldown (which was formerly 30s). They have Whispering Dawn... that's a passive heal on a 60s timer.
When people balk at these suggestions I'm making, they seem to do it under the assumption that I have no idea how to play SCH. I cleared O1s and O2s in the first week with my static. Sure, you can argue those are the easiest encounters this raid tier, but we cleared them after 9 hours of work - 3 hours for 3 days. We are not hardcore. We're midcore at best. However, to clear these two raid tiers so fast means that I do have some idea of what I'm talking about. Yeah, I avoid using my GCD heals as much as possible. I rely on my fairy cooldowns and oGCD cooldowns a lot. I've timed for when to specifically fire off my heals for their most optimal use.
It's for when things go wrong and my plan is interrupted that SCH lacks the flexibility to recover that the other two have. SCH has almost 0 wiggle room for mistakes by the rest of the party, even worse its own. If I die and Aetherflow's on cooldown, I'm pretty much still dead. I have almost 0 healing potential because the little bit of MP I get from being revived has to go into resummoning my fairy. I have to beg my party for MP, even if Lucid happens to be ready to use. Sure, you can argue, "Well, don't mess up." Yeah, and we live in a world where pencils don't come with erasers.