I will agree with you on the discussion involving Arrow, as it does need more proper math involved to fully determine its total percent damage increase as it does affect more than just simply spell speed casts, but on the whole, the math become superfluous if we take into account that Balance is the best card for flat party increase as that's what it's designed around. You could try to argue it's not due to the lack of math, but too much related to AST requires perfect hypothetical situations which practically never arise to begin with. If you do want to argue towards the classes fullest potential, fine, but that's all it is. Potential. Other classes are too definitive in their buffs for AST to truly be worth it.
Arguing in favor of Spear is laughable simply because you cannot demand that you measure things based off RNG and then throw in a perfect hypothetical situation in which Spear is always used at the correct time to draw upon its maximum benefit of shortening cooldowns. The fact is while you can also scribble all the math you want in a vague attempt to decipher Spear's true "power," fights and battles in FFXIV all require DPS to use their cooldowns at very specific times, and there's almost no guarantee you're going to pull Spear at the right time in order to utilize it properly. You'd either be waiting around for a good time to use it (DPS loss), forcing the DPS to not use their abilities (DPS loss), or burn through various other cards in an attempt to draw it (DPS loss.)
Spire is not worth calculating in any sense simply because TP is never an issue. Spire would only serve as a true benefit to DPS increased if the target you are using it on eventually burns and runs out of TP, which is never the case. If you use a Spire on a Monk and they still have TP left, it was a DPS loss and waste as they never properly took full advantage of what the card had to offer, simply because if you're never running out of TP (which never amounts to a DPS loss), why would you need a buff to reduce TP costs if TP is never an issue?
I'll spare Ewer simply because of its use for Black Mage, but again, you yourself can argue against the math performed already (which I agree is a tad on the weaker side without any readily available computations for analyzing), but you can't simply state, "Well, of course you'll have to measure EVERYTHING" because if you really want to measure -perfect- scenarios, Balance is the most reliable increase in damage, and anything less simply isn't worth measuring because it's not the maximum potential AST can bring.
You could argue, "Oh but Ewer is a DPS increase as well," but it doesn't matter. Who cares if Ewer is a .01% increase? It's less than Balance and it isn't even worth mentioning because you're not reaching AST's full potential.
So while you could do all the math in the world, it's not going to magically make AST any better. It requires too many perfect scenarios, too many perfect draws, too many perfect things, where as other buffs from other classes are set in stone. AST, unfortunately, does not have that luxury, and the cards need a buff in their overall DPS increase to show that.

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