Its all personal opinion but about the gauge is mainly because it can give more depth to the fairy skills than only being limited by a cooldown. It could allow for a more interesting resource management, it would be build and spend yes but if properly managed it could lead to Sch having to think more deeply about the efficiency of the tools vs their effectiveness in the short and long term, allowing smart and efficient Sch to rely more on their pets than less experienced ones and as such giving a skill ceiling in the healing that is not simply "do not use X unless you dont have anything else"and because right now is used in a way that has very little impact on Sch gameplay when one could think that in a pet healer a pet related gauge would be something big. (I have an old example of how I'd envisioned that gauge in this forum that could give a better idea of what I talk about, keep in mind it was before EW tho)
About Aetherflow:
Because it does not fit the current game, the game is moving to a place where more free healing is happening than ever and Aetherflow in its current iteration only serves to punish Sch when used to fulfil its role. One could argue that it serves as a way to force Sch to really think about the way they approach their healing and while that is to some extent true the approach is very rarely something more deep than "not use it" instead of "use X instead of Y" is not that much of depth, if healing is a puzzle "do not use this piece that is core to the job" shoudn't be the correct solution that often, worst of all is that in relevant content the Sch is rarely the one paying for its own mistakes as is usually the cohealer who has to pick up the slack. One could also argue that is allows Sch for more dps depth but imo that should come from its own dps rotation and not from a tool that penalize it for healing, especially when once again, if the healing is not done properly more often than not the Sch is not the one paying the consequences
About the flexibility sorry but I disagree, Addersgall and Aetherflow are the exact same thing with the only difference being that one does not penalize the job that interacts with the system and as such all of the tools in it are used more frequently while the other penalize its use on any heal, look at the parses and see out of all the aetherflow how many are used on ED vs the rest of actions if they are used at all (Spoiler: Top Sch in P4s only use AE to heal once and left its cohealer deal almost twice as much healing as they did). The current Aetherflow design creates a dominant strategy within the mechanic of using it in ED in almost its entirely while Addersgall allow for its tools to have breathing room where they all can see use (Same argument with Lillies with the difference of not being so quite the exact same thing and its use being encouraged more as it makes the job not only more capable of healing but also allows for smart Whm to capitalize raid buffs).