AST cards in raid

[Kaisersoke]

In response to your mchs and ninjas.. they should NEVER hold on to cooldowns for "burst phases" unless its the hands in as3, and spear also affects mudra cooldown, allowing ninja to use another ninjutsu before the 20s mark, which is a dps increase no matter what angle you look at it.
If you dont have a RR youre saving and you draw a bole.. just throw it on the tank anyways. you can solo heal in that time so your co-healer can dps. you might not feel the effects, but theyre there. they help. no sense in burning too many cards, youre gimping yourself.

Ewer is immensly powerful, especially on summoners, or your co-healer. or yourself. More mana=more wiggle room, or for the summoner, if theyre good, they will realize you ewer'd them, and they will throw out extra ruin III. dps increase. if neither are applicable, RR fodder for Expanded.

Spire is considerably less useful, but if no DoW are hurting for tp, more expanded RR fodder. but as you said, your melee swap the gob, whereas if you threw a spire on your monk (who is much better aoe and single target damage than dragoon) they would be able to dps longer. dps increase.

all of your cards are dps increases one way or another, the more of them you burn on royal road, the more dps loss you incur. royal road and shuffle both should be used for strategic buffing, setting up for phases that require heavy dps, heavy healing, etc.
spreads go to arrow/balance first and foremost, or spear/ewer situationally. an expanded spear on pull is WAY underrated.

example: Youre on oppressor savage, .5 has yet to come out, you have an arrow on spread, no current royal road, and you draw a bole. shuffle is ready to be used, and a tankbuster is coming up soon.

your options now are extensive. you could toss the bole on the tank, and save the arrow for the next draw, hopeful for an ewer/spire.
you could shuffle the bole for a hopeful ewer/spire for some serious raidwide dps before .5 comes out.
you could royal road the bole and arrow a dps for a more reliable dps increase (because you wont always get expanded rr)

the strengths of AST is mainly in how many options it has, but making the wrong decisions is also a major weakness of AST. It has amazing potential, and you shouldnt downplay the potential of any of your cards. they are all very strong, albeit not always in the same ways.

[Elth]

Spire is considerably less useful, but if no DoW are hurting for tp, more expanded RR fodder. but as you said, your melee swap the gob, whereas if you threw a spire on your monk (who is much better aoe and single target damage than dragoon) they would be able to dps longer. dps increase.

Yeah no, you don't change a well rounded strat on the RNG factor of Spire cards, they're used to swap drivers at a fixed wave no matter how much spire i threw on them, which could be 5 or zero.

example: Youre on oppressor savage, .5 has yet to come out, you have an arrow on spread, no current royal road, and you draw a bole. shuffle is ready to be used, and a tankbuster is coming up soon.

your options now are extensive. you could toss the bole on the tank, and save the arrow for the next draw, hopeful for an ewer/spire.
you could shuffle the bole for a hopeful ewer/spire for some serious raidwide dps before .5 comes out.
you could royal road the bole and arrow a dps for a more reliable dps increase (because you wont always get expanded rr)

Love your exemple there. If a RR the bole and Arrow a DPS, there sure will be a DPS increase BUT in the event the next one is Spire/Ewer i'll feel screwed. Bole doesn't make enough of a difference as i said to use it (especially on that fight where the only hard hitting ability is Hypercompressed plasma, and everything else is healed with either Benefic 1 on tanks, AH/Helios on raid and Synastry on preys.)
In that exemple, using Bole yields almost no benefit, Shuffle is always a good option to get Ewer/Spire and RR is the second best one. Let's say i RR'd the Bole, next turn i'll have either :
-DPS card, throw the enhanced DPS on single target while keeping the arrow in your spread for AoE (and still remains true for every next draw)
-Spear/another bole, In that case yeah, might as well throw it on the right target (namely MCH/NIN or Tank) BUT will wield almost no benefit so RR or using it will almost be the same when you look at the big picture (a 10min long fight)
-Spire/Ewer give that opportunity to, yes, override the bole RR buff BUT allows to AoE the Arrow.

For a "waste" of 30s (Draw cooldown) in your exemple, by RRing the Bole I effectively went from one good option (single target enhanced arrow) to two good options (enhanced arrow OR AoE arrow) and a "meh, don't care much" one.

Now A1 and A2 are on farming phase for pretty much every raiding guild, A3 is still an issue but close to farm aswell, A4 is still an issue for most. (At least from what i've seen). Means that (edit : in my group) in A1 A2 people are so overgeared that TP/MP management is not an issue anymore, Bole is almost never noticeable, Spear is useful for the pull but will almost always be wasted midfight (CDs already on cooldown or DPS will hold onto those CDs for the next burn phase). On A3, hands don't hit hard enough for Bole to make a difference on a single tank, and most of the big damage (namely raidwide slap to the face and x6splash and Cascade on P4) will be healed in AoE until pretty much everyone is topped off (or will be with MII soon), a case where only the tank taking slightly less damage (and everyone else eating their own teeth) is effectively useless. Same for A4's Carnage zero, or that big ball of doom everyone has to take.

Ewer is the only one we can argue about, but let's face it : BLM, SCH and SMN couldn't care less, my very own WHM tells me that he doesn't feel any difference, the only good target being myself... and i dont see the point of using a potential AoE DPS increase to make up for my own mistakes in mana management. So yeah... looking at the big picture (pretty long fights) i just can't see a lot of moments where using the "lesser" cards is that much better than discarding them to enhance the good ones (that may never come, but come on... they'll come at least a few times unless incredibly bad luck)
(Keep in mind that i told in the OP that i know they're situational and SOMETIMES, when the stars align and you get the right card with the right buff at the right moment those lesser cards turn into good ones. But the chart was here to explain my vision of those things in MOST cases.)

Few numbers in exemple:
On a PLD, Living liquid hits (in single target) from 2.4k to 3.7k damage. My Benefic I heals for 3.5k (~5k crit). 10% dmg mitigation with Bole would turn those damage from 2100 to 3330. I can still heal that in one Benefic I. Every other ability that does MORE than those damages are in AoE and will be healed in AoE regardless of how much the tank has taken (which will probably be less than everyone else considering their own mitigation).
Even if i was less geared and Benefic I was healing for only... i dunno, 2.8k maybe (i think it was the value in law gear) it still wouldn't be good enough to spare me more than 2 or 3 heals on its full duration. Now, yeah, there are tank bursters. And Bole, if drew right before that tank burster (in the 15s before it actually) could and should be used. How often does that happen ?