Let me preface this by saying that I'm a Scholar main who has cleared current Savage content, that I've been playing it since Stormblood, and I absolutely love the class. I don't have the experience of some, but what I do have is a perspective that might help move the conversation forward.
In the furor over the controversy in Scholar vs Sage, there is one comment that has gone underexplored. In the Letter From the Producer on September 17, Yoshida stated "There isn't much that we can change about Scholar, significantly."
This is the core problem with Scholar. For the past few expansions, Scholar hasn't changed significantly. There has been the Seraph upgrade, of course, but the basic formula of "Fairy heals, Scholar does GCD shields/oGCD heals and attacks" hasn't significantly changed. Compare this to Astrologian (who has seen the cards reworked, gotten a change from more time-based powers to more star-based powers, and so on) to White Mage (who has gotten THE BLOOD LILY.) Scholar seems to suffer from lack of inspiration, and so has less from the developers.
Let's explore some options, and see where Scholar can be.
Scholar is, more than anything, a healer forged in the fires of war. They are made to enable small groups of individuals to succeed against overwhelming odds. They were capable of standing against incredible threats and bringing their team through. That should be the basic feel of the class: the Scholar is the heart of the party who keeps it safe and can rally the party to victory. So, let's explore some options.
1. Barrier Buffer. The Scholar was the reason Nym's marines went against other magic-powered city-states and won. This could be as simple as barriers giving buffs while active (this would encourage GCD barrier usage, as well as make Seraph even more of a major event,) or being able to trade a barrier for a buff, or any number of things that reward teamwork.
2. Teamwork. Right now, the most powerful aspect of Scholar is Chain Stratagem. That's in the right vein, but right now, it's not particularly engaging. It might be more useful to have both the Scholar and the faerie aid the party when they aren't required to heal. Faerie Gauge could be spent to buff allies, similar to how Selene used to work, thus leading to synergy between Scholar and faerie and party. The idea being that the Scholar should be the heart of the party, one who everyone is drawing attention from. For that matter, instead of 'Chain Stratagem', it could be more like 'Call the Charge' or the like, making it clear that the Scholar is working with others.
3. Safe Zones. Now that White Mage has gotten two zones, it opens up Scholar as having their theme based around terrain and position. They could create zones where enemies are weakened or allies are buffed, similar to the sacred standards and idols of the Mamool Ja. This would further emphasize the Scholar as a tactical class, while being vibrantly different from others.
4. Channeling Abilities. We already have the faerie healing allies with Fey Union. Instead of using faerie gauge purely for healing, it could be used for buffs as well. Basically, the Scholar has an option: the faerie can heal someone while the Scholar focuses on damage, or the Scholar can barrier/oGCD heal while the faerie buffs an ally. There's an option that strengthens the feel of the Scholar as a healer and the synergy with the faerie and the party, exactly as the Scholar should be.
Those are just ideas off of the top of my head, but the important thing is this. Any of those ideas could anchor a class. Any of them could also be added to flesh out a class as it is. And all of them would be, if properly implemented, an improvement to Scholar as the flavor would have it, while differentiating it from other classes.
That's why a lot of people like me are upset about Scholar. It's not about the mechanics, though that's part of it. It's that there's a lot of untapped potential that seems to be ignored, while other classes are overflowing with inspiration. If this post has caused even a bit of such inspiration for the class I've grown fond of, then I couldn't ask any more than that.
Not to say any of your ideas are bad, because they're good ideas! I just want to say that I'm honestly really happy with how the job plays right now, and I think it's the most engaging healer. I honestly think the problem is Scholar's VFX aren't as flashy as the other jobs. People have been most consistently excited and wowed by the other two healer's particle effects. For scholar, the most beautiful ability we have is excogitation (which is gorgeous). I think maybe a VFX rework would help!