It's important to recognize that shields are a tool players are given to deal with one specific mechanic: lethal damage.
Lethal damage is very difficult to balance. It will present a hard wall to the party if not resolved. It is avoided in casual content (both raid wide and singe target) because the devs cannot assume that someone will adequately counter it. Try it out in your next dungeon or normal trial/raid. Both raid wide damage and tankbusters will fail to fully deplete HP bars even at low item levels.
The next step up, Extreme trials, will occasionally use lethal damage. Most of the time it will be a tankbuster that must be mitigated, however some transitions will also be lethal to minimally geared party members without some mitigation. Generally one defensive cooldown or shield will be sufficient. Regular raid wide attacks will almost never be lethal unless someone has acquired two or more vulnerability stacks.
In savage and ultimate almost all tankbusters and raid wide hits will require stacked cooldowns or shields to survive. At minimum item levels a single hit could require as many as four sources of mitigation simultaneously to survive. Lethal damage occurs more frequently and the party must spread out their cooldowns if they want to survive.
With how frequently mitigation is needed in top level raiding, why is it that shields are rarely needed? Simply put, tanks and dps have more efficient ways to mitigate lethal damage.
A normal raid team is going to reliably have two tanks', one melee's, one ranged's, and one caster's worth of mitigation tools. The tanks will use their personal defensive and single target mitigation tools to deal with tankbusters and autoattacks. That leaves their raid wide mitigation to help the party. This will consist of two Reprisals every minute and two job specific cooldowns that either reduce damage by 10% or apply a roughly equivalent shield every 90 seconds. The melee dps will contribute Feint for -10% on a physical attack every 90 seconds. The caster's Addle is the same thing, but for magic damage. All of the ranged jobs have a -10% damage tool on a two minute cooldown. A fourth dps will provide more cooldowns, but will be omitted for the purposes of this exercise.
Over a six minute period this works out to 14x -10% damage CDs, 8x tank job CDs (generally around 10%), 4x -10% physical CDs, and 4x -10% magic CDs. If lethal damage occurs every 30 seconds and each instance of damage requires three cooldowns to safely mitigate it, then 36 defensive cooldowns are needed in total. That's only six more cooldowns than the tanks and dps provide. This would leave healers responsible for shielding once per minute, except healers ALSO have mitigation tools. WHM's Temperance can be used every two minutes. SCH's Sacred Soil can be placed three times per minute (at the cost of Energy Drain or other healing abilities) and Consolation provides shields twice every two minutes. AST can Collective Unconscious every minute and, if Nocturnal, apply a shield with Celestial Opposition every minute. Each healer has anywhere from three to twelve free mitigation cooldowns over that same six minute period.
All of those cooldowns are oGCD and most of them can be weaved with no loss of uptime. Addle and Feint will sometimes align badly with the player's rotation and Temperance may require clipping a Glare if it isn't properly planned in advance. Tank CDs are completely free to use. Compared to this the GCD shields (Succor, Aspected Helios) are costly in terms of time and mana. Losing a GCD to do the same thing that the rest of the party weaves painlessly makes shielding spells lower priority. The mana cost can lead to the healer running dry later in the fight.
Despite these costs, GCD shields serve a purpose. Healers' on-demand shields can help make up other party members who are less diligent about mitigating lethal damage. If a CD is used at the wrong time a GCD shield can be used to replace it. They can also be used if someone fails a mechanic and has vulnerability. The nature of raid bosses is that their lethal mechanics do not perfectly align to the party's resources. The specific timing of a boss fight will lead to CDs being held. Multiple lethal attacks will occur in a short time, forcing the party to rely on shields to spread out their cooldowns.
I would posit that the problem with shields that they are unnecessary so much as their being unnecessary diminishes the healer's role in party survival. The easiest solutions to this that I can see are to 1) increase the frequency of lethal damage (mitigate more often), 2) increase the severity of lethal damage (mitigate more per mechanic), or 3) tweak the ratio of mitigation cooldowns towards healers by either granting healers more CDs or removing some from tanks and dps. The end result of all three is to introduce more lethal damage that cannot be covered by the rest of the party.
My personal preference would be a combination of the second and third. Increase lethal damage in casual content to require a single source of mitigation, two sources in extreme, and up to five in savage and ultimate. Give all three healers a passive trait that grants the party -10% damage taken based on another tool they have. Throwing out ideas, WHM could give anyone healed by a Lily -10% damage taken for five seconds, SCH could grant -10% for five seconds to the party after spending aetherflow, and AST could grant -5% damage to allies standing in their Earthly Star (weaker because longer duration). Ideally healing best practices would grant more resources. WHM's Glares, SCH's dot ticks, and AST playing cards on the correct players could all build resources that could be spent for party mitigation or oGCD shielding. For single target applications WHM's Divine Benison could be twice as potent when applied to a player under the effects of Regen, SCH's Adlo could automatically crit targets with Excog, and AST's Synastry could confer a percentage mitigation and possibly increase the percentage if a card is played on that target.