About the WAR TP, that's my point. WAR didn't need Equilibrium's TP. It is a point of exaggeration. WAR's TP is an endless pit without Equilibrium unless the WAR has to spam Overpower for whatever reason. Since that is irrelevant to raids (A2S and T4 being the only exceptions), it doesn't matter. People thinking WAR is a better OT because of Equilibrium is just baseless and stupid.
WAR is better suited for MT than it is OT. WAR has the most available damage mitigation options. WAR has the easiest time stance swapping allowing it to "fit in" bursts of damage or mitigation as needed. This same point leads to highest MT DPS. Only problem to WAR MT is its strict GCD to GCD management putting it at being a riskier option than the other two.
PLD on the other hand is better suited for OT. PLD's CDs are strong but they are also long. PLD has massive utility they can access easier as OT than MT. Cover is OP.
DRK is the black sheep. It suffers badly in physical fights. It runs out of TP very fast as an OT too with no options to mitigate TP expenditure. It is currently made relevant because it handles magical bursts slightly better than PLD with a 10~30% more mitigation per buster. But that nets you less than 5% overall damage taken difference. If DRK didn't do 2~3% more DPS than PLD and the majority of tank busters weren't magical, DRK would be the one out of place in current content. That is an underlying problem that seriously needs attention from SE imo.
EDIT: In the best CD rotations, DRK hardly mitigates 8% more than PLD on any single Buster. And on some it mitigates 100% less (Since PLD uses HG in its rotations now). For reference on numbers and examples on rotations: Check this post(also by me).
AST being sup-bar to SCHs and WHMs can be attributed to the things you mentioned. But also let's not forget that WHM's more potent multi Regen effects and SCH's more potent heals/shields along with Fairy support healing allows for less hands on healing and more DPS while an AST can't afford to stop healing.
SE gave a "good" reason why AST shouldn't heal as much as WHM and SCH in vacuum. The card buffs ARE strong. But card buffs suffer from RNG and you can't have the card you want when you want it. Furthermore, AST is hindered by far more things than just healing potency. AST single target DPS is lower than WHM and its AoE DPS is lowest among the three.
IMO AST needs major fixes. DRK needs to be looked at on different levels. PLD is fine but QoL changes are always welcome. I do not mind more DPS on PLD if it forgoes some of its safety.