Foremost, this isn't about the validity of Sch as a healer. Second, there is definitely a tl;dr at the bottom. Sch is in a much better position thanks to 4.05. They can do pretty much anything the other two can do. No, the viability of Sch, at least from me, is not in question since 4.05 dropped. This is something else entirely.
I'm going to start with the roots of Scholar in FF in XIV. 2.X was a simpler time in terms of identity. I'm talking about a time to when Warrior didn't even have that “Health will not go below 1” effect at all on Holmgang and Lustrate was a “20% of the target's total hp” heal. During this time, you always wanted to combo a Whm and a Sch for the pure throughput healing and mitigation with damage combo. Sch was the more difficult one to play than Whm, since they had to micro the fairy and they didn't have the throughput healing. This was fine, since they used shields and damaging enemies to keep damage down while fairy (which has always been a glorified regen that you have to babysit and argue with to make them work well while our overall potencies are reduced to take her into account) used her heal as a type of mitigation to prolong our dps. Whm was the perfect main healer, and Sch was the perfect off-healer. Doing damage as a healer during this time was an uncommon thing. It showed that you knew the limits of your job when stance dancing with Cleric Stance. These two were taken for their specific roles. They had concrete foundations for SE to build upon later.
Heavensward came and SE did a pretty good job at expanding their two core healers, but this is also where things started to make the lines blur. White mage got more AoE heals, making it even better at party/alliance healing. Astro...was lagging behind everywhere. Sch was changed a bit with Lustrate having a potency, getting an AoE Aether heal in Indom, and then the Emergency Tactics for those times where pure healing was needed. This is where I think it started. We were getting more and more throughput heals instead of focusing more on our core mechanic of shielding. Critlo deploys were basically our way of dealing with great amounts of damage, but I don't think it was inherently overpowered. Having to fish for it, getting everyone gathered when it happened, and Deployment Tactics being on a 1min cooldown was the price. Not too difficult to deal with in an organized group, but helped greatly with our lack of aoe throughput and even helped Whm's mp problems. I'm definitely not saying Sch didn't need the nerfs. I would have been the first to take a swing with the bat, but more on that later. Towards the end, with 3.4, Astro got up there with everyone else, and I was honestly happy to see more of them as co-healers, but they were now starting to become a problem. Their shields were getting stronger and stronger, and their cards buffing the entire raid was making them almost a necessary pick. I had a few Astros that would even refuse to use Diurnal because “My shields are stronger than yours”.
This continued into Stormblood, as well, since Astros get a bonus to healing based upon their sect, and get flat healing-to-shield percentages. Our shields are a flat 300/300 (hp/shield) unless crit, in which case it goes to 300/600. Astros shields are a flat 200/500 (230/575 once the healing bonus from being in Noct Sect is factored in). Sch's 600 (900 crit) vs Astros 805 potency shields is not a good sign for the class that has the shields as its core mechanic. Sure, when they crit, it is ~100 more potency, but crits for 100 more potency vs constant 200 more potency has a clear winner in that Astro is far better at our core class concept than us. This, along with losing some our constant dots, cleric stance (which is basically losing 10% damage), bane being (and still is) left in shambles, a loss to Blizzard II, having to use an mp refresh along the nerfed aetherflow, our shield mana costs, and the nerf to Embrace left Sch a mess. This was the healer that did damage as a form of mitigation, and now needed to spend everything in it's power to keep the tanks alive. This was pretty jarring. This basically turned us into weaker versions of the other two healers. I don't think SE thought of all of this through. It's almost like they thought nerfing our damage from multiple sources (increasing fight times), nerfing Embrace (which makes us heal more), and making our shields cost an arm and a leg (which we relied on) wasn't going to make us spend more time and resources in fights healing, while doing less damage, and basically turning each pull into a slow war of attrition.
That looks like I have a bone to pick with Astro, but I don't, really! Astros are fun to play, and they have their cards, which is a very unique and involved thing. I do really wish they had made Astro's healing style more unique instead of SE being too afraid to break the heal/shield meta. Who knows what kind of healing the Astro could have gotten if they weren't given the Sects? It could have even made them not bad at the start of Heavensward. The fact that they have the Sects, though puts them in a vacuum of “Well, they don't have the regens/shields of Whm/Sch”, which leads to further balancing issues.
Patch 4.5 arrives, and it brings us up to the other healers while trying to make things less clunky. Great, right? Well...yes and no. My problem is that these adjustments only further tuned our pure hp healing. It did nothing for the core mechanic of our job, which is using our shields to mitigate damage. This has left Sch in what some have called an “identity crisis”, and I, for one, definitely agree. Why do we need yet another healer that can just plainly heal everyone? We already have a Whm who does this extremely well, and manages to be fun while doing it. We are proactive healers, not reactive. SE has slapped a band-aid on our skills that comes in the form of making us closer to being more of hps healers like a Whm that has three resource points to spend in place of mp. That is making the lines of both of our class's blur even more. What is the fun in playing another class that functions so closely to the other of the type? That is like giving a Sam Drg's Dragon Eye, but they must spend some Kenki to activate to fix it not having any utility.
Even though someone can probably think of better examples, that isn't how class balancing should be handled. Improving upon the job's core concept is the first thing that should be done. This makes the class stand out more, which makes them excel in differing areas, which makes party compositions more fun and varied, which makes the classes more fun. I get that Yoshi is trying to bring the “skill ceiling and floor” closer together for those that are very casual, but noone wants all the classes to perform the same. Sch was always a more difficult healer to master, much like Drk was a more difficult tank to master, and Smn/Mch were more difficult dps to master (these, of course, are my opinion of them at their highest levels of play). This made them fun and rewarding. Some classes should be more difficult to master to others and feel rewarding to play when performing them to their utmost. It makes it a goal for people who really want to play the class, and a constant challenge for those who know how to play them. This has been taken away with many of the classes trying to be brought to almost the same exact levels across the board. There should be more variance in their strengths and weaknesses, but to the point of where we see people arguing about the “best” party comps and not have a definitive winner.
TL;DR: Sch is perfectly viable, but is in an “identity crisis” since it is becoming more and more of a throughput healer instead of being the mitigation/damaging healer it was since 2.0. This is making it less interesting/fun while highlighting the clunkiness that has always been present since 2.0.