Just some random musings,
I'm not going to address the "lack of healing capabilities" of an AST, mostly because I haven't played and experienced one myself.
On the other hand tho regarding the 6 drawn cards, is it possible that these seems underwhelming due to lack of communication?
Imagine a well oiled team where everybody's communicating via voice comms, as an AST you can announce which card you obtained, and who'll benefit most from that card.
Just a few examples to illustrate my point:
Got Arrow (10% attack speed) and a WAR is just about to pop his berserk? Slap it on him so he can get 1 or 2 more GCDs in.
Balance (10% damage), find out which dps is about to activate their CDs for burst damage, and give it to him.
Spear (20% Recast), maybe that summoner who's just Raging Strike-ed, and about to unleash all his/her festers, slap this on him, instead of 2 festers per RS, it is now possible to unload all 3 festers in the RS duration.
Obviously all these are extremely situational, but there's always the chance of some awesome synergy wombo-combo happening every 30 seconds.
All of the above is most likely unattainable in a random DF party, but if SE were to adjust these buffs based on a random DF party, I honestly cannot imagine how frighteningly powerful an AST can be in a well oiled team.