So, I'm of two minds on this topic.
On the one-hand, I agree that a lot of healer kits feel very same-y in terms of offerings. You've got your DoT and single-target attack, your AoE attack, two ranks of single-target heal, two ranks of AoE heal, and an assortment of CDs (one of which is another attack).
On the other hand... I also understand why the kits are same-y like that. From a damage-dealing perspective, a healer's kit shouldn't necessarily be too complex in that regard, largely because their core focus isn't on dealing damage and they should avoid being distracted by a rotation when they may need to drop everything at a moment's notice to spam heals on the tank, especially when any level of complexity in their damage rotation wouldn't necessarily be rewarded with particularly high output. From a healing perspective, every healer position has basic requirements and breakpoints they need to meet/fulfill, and by allowing them to have similar basic kits, it's easier to balance them against one another and balance encounters around the assumption that each healer has the necessary tools for each curveball; meanwhile putting a "rotation" on healing also limits their ability to respond to damage output without "breaking" the rotation.
Considering AST has Lightspeed, Gravity and Regen, still casts damage buffs on the party, and only recently lost the ability to extend its buff timers or grant specifically attack speed (the latter because literally only BLM wants it anyway), I would be severely disappointed if they went and made Time Mage, much more so as another healer competing with AST that took tools away from it, especially while there are still untapped alternative options that don't step on existing healers' toes/themes/kits.
Bear in mind that "Time Mage" is a misnomer, since the job has always been about time and space magic (shown through access to Gravity, Float, Comet/Meteor, etc), which remains the domain of the AST.