Triple Triad allows you to make better decks as you play. Why not the same for AST? A big part of AST's draw is that it features the card system and ways to manipulate the odds. In a lot of cases, you just never get the card you need, so a lot of that potential goes wasted between getting a second (or the same) unfavorable card with Shuffle or having nothing better to do than play it or burn it via Royal Road.
So how about deck customization? As you level up, I propose you unlock traits that allow you to build better decks. This would allow you to swap out unfavorable cards for other ones.
Our star globes have 12 cards floating around them. For the purpose of this suggestion, let's say our deck has 12 cards in it. The chance of drawing any one type of card would be 2/12 (1/6). Let's say that with our job traits we can start swapping cards out. So we could remove one Spear and replace it with a Bole, meaning we have a 1/12 chance to draw the Spear and a 3/12 chance to replace the Bole. We could remove both Spears and make the Bole and Ewer each have a 3/12 chance to be drawn.
I would propose that the max level trait would allow you to swap 4 cards out of your deck for others. You could weight these mostly evenly between other cards if you wanted or go all in to get more predictable results. Some feasible decks under this max level job trait would be:
DPS deck, perfect for quick dungeon runs:
Balance: 4
Bole: 0
Arrow: 4
Spear: 0
Ewer: 2
Spire: 2
Tankbuster Deck, for when the Hulkbuster isn't enough:
Balance: 1
Bole: 6
Arrow: 1
Spear: 0
Ewer: 2
Spire: 2
Balanced deck with no Spear, weight what you want to prioritize:
Balance: 3
Bole: 1
Arrow: 3
Spear: 0
Ewer: 1
Spire: 4
The "we have no magic DPS and a WAR tank" deck:
Balance: 4
Bole: 1
Arrow: 3
Spear: 0
Ewer: 0
Spire: 4
Essentially, you could create multiple pre-made decks for the type of content you want to run. This would better enable the AST to support various party compositions in various fights. As you might guess, I'm not a big fan of Spear; it's useful in some situations, but you won't find yourself readily drawing it *exactly* when you need it.
As far as slotting cards ahead of time would work out, this is not a new mechanic. Final Fantasy XI did this with blue mage spells, and EverQuest did this with basically all the casters. I am just merely proposing having multiple decks like the Triple Triad system that you can swap between before (but not during) combat.