Since you want to know why people even liked the HW/SB cards, I'll share my perspective.
First off, I don't care about damage, never have, what I care about is whether or not I can make an impact in the group. I don't remember the perfect runs where I get 2 melee/1 range cards every 2 mins and every Sleeve Draw is a Lord, I do remember the runs where I enhanced a Bole and saved the tank that screwed up their CD rotation. Cards being all damage simply lacks immediately obvious impact, you maybe end the fight about a minute faster if you have a perfect run, but that's not as immediately obvious of an impact as, say, dropping an enhanced Ewer on your cohealer that just raised and is starving for resources.
Another point is that I like having the randomness of what I'll Draw and being given the tools to manipulate my way to the goal I want. I enjoyed that HW/SB AST gave me a goal (AoE Balance) and gave me the tools (Royal Road, Spread, Redraw, Sleeve Draw) to work towards that. I view ShB/EW cards as being given the victory (a damage increase) by default, you didn't work for it, you didn't fight for it, it's just handed to you. I loved manipulating the cards to reach my preferred outcome while also thinking about it every step of the way and what I would do for the next card. For current AST, part of the thought process is entirely gone, I only need to briefly think about alignment with job damage profiles, I do not need to think about what I'm going to be doing to get to the next payload because I know I'm being handed it for free every 2 minutes.
I know HW/SB cards wouldn't work in the current game because some of their effects are already rendered obsolete (Spire, Ewer) and some are basically not needed (Bole, Arrow), but that doesn't mean that every card HAS to be just a flat damage increase. Separating Draw into offensive and defensive buffs is an option. Cutting out most of our pointless heal buttons and giving us more ways to work with the card system to get to our preferred goal (whether it be AoE Balance or an Enhanced Bole for the really bad tank) is also an option. The dev team could be creative, but my problem with that is they just aren't.