Who else is worried about SE and Ast?

[YusiKha]

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Or, like NIN and SMN, make Play a GCD.
Even a short GCD like Meditate would give you more time to switch targets (2.5s to target an ally, 1.2-2.5s to go back to the foe).

[Lastelli]

Or, like NIN and SMN, make Play a GCD.
Even a short GCD like Meditate would give you more time to switch targets (2.5s to target an ally, 1.2-2.5s to go back to the foe).

That would change very little, I'm afraid.
Currently, you need to press a minimum of 3 to a maximum of 6 buttons to give a card to a dps player + 1 more button to go back to the boss if you're dpsing or 3-4 buttons to target the tank if you need to st heal them. Your suggestion would give a little more time (like and extra second) to deal with those buttons after you played the card, but the amount of buttons to press would still be a little overwhelming, especially when compared with what the other two healers have to deal with.
A quick look at healers' CPM (which doesn't include target shifting) makes it glaringly obvious that AST is pressing way too many buttons right now when played correctly, and something should be done to address this; AST currently has to press more buttons than any other caster and most dps jobs if you're playing with a controller. Controller users can't even use macros because they'd need 4 macros for play and 4 for minor arcana, and at that point the button bloat would be unbearable.

I think this will only really be useful in high end gameplay or with statics. For DF or PF content I don't know before the battle runs for a while who the "best DPS" even is. For example if I put it on a BLM and MNK and after a minute I notice how the BLM is an ice mage and the MNK ignores positionals, I can't put that buff on another DPS. If I even managed to in the first place, because someone pulled the boss immediately anyway. It may work theoretically, but I can already see me being annoyed at it.

I'd rather have Sleeve Draw replaced with a skill that makes the next card AoE or something like that.

You're not wrong, but I'm not sure tunnig skills around the possibility of having terrible players in your party is a good ide. As long as other party members are not totally incompetent, the difference is actually very small. Also, that's why I included the possibility of manually selecting a party member and override the effect of the buff: if you realize that you gave the favor (or whatever you wanna call it) to a bad player, you can just select another player and keep playing as you'd do now. And after the inevitable wipe caused by the bad player, change the target for the favors.