Even if the Spear were to be redesigned in the way I wanted it redesigned, my Spread would still be better used holding other cards, which I already pointed out in my post.
I mostly hold Balances because a lot of the groups I join (and my static) want the extra DPS to push phases and maximize group DPS. I hold Boles for tanks or for a phase such as Susano Ex's Sword phase to minimize outgoing damage so that I may contribute to DPS, and not have to heal as frequently. I also hold Ewers for myself if I find myself in a group or piece of content where my MP is being strained. Occasionally, I will hold an Arrow if I cannot draw a Balance, and attempt to Expand the Arrow, or Enhance it if I am with a BLM, since a lot of them seem to ask me directly for Enhanced Arrows nowadays (all those Fire IVs, I suppose).
Again, my Spread is never used on a Spear. Because the card is too situational to use, especially with its current design, and you run into it taking up time in your Spread when you could be holding other cards. To expand on this: Lucid and Celestial both have 120 second cooldowns. Even if you were to draw a Spear and use it on yourself before using those two skills, and 30 seconds later draw another Spear and hold it in your Spread, there will still be an entire minute before you could even use the held Spear on Lucid+CO again. An entire minute where you could be holding a Balance to expand to the group for a DPS check, a Bole to toss on a tank that needs it for an upcoming tankbuster, or a Ewer to toss on yourself, your co-healer, or maybe even a SMN or RDM that were killed and need a little bit of MP to get back on their feet. To be honest, it's an almost selfish thing to do, because, like myself and others have said, you cannot know (especially when paired with randoms) when your party members are going to use their cooldowns, or when they would need or even want a Spear for them. So you would essentially just be holding the card for yourself, rather than using your Spread to try and optimize your team. And, to me, that is selfish.
Yes, I am one of those ASTs that DPS as often as I can. I do not like being forced into the "main healer" role, and I firmly believe that both healers in 8-man settings should contribute equally to healing and DPS, regardless of the job they are playing.
When you join, for example, farm parties in PF, most if not all of them are looking for clean, fast runs so that they can squeeze in as many clears as possible with the time they have to farm. AOE Balance, even if you think it's silly, achieves this goal. Plus, a lot of people care about their own personal DPS numbers, and will never ever say no to a Balance. That's a given, regardless of whatever potency Balance is changed to if SE decides that it needs rebalanced. The majority of the playerbase is the one with this mindset, and that is not something that will be easily changed.
While I always stress for people to learn mechanics and never expect to outright skip them (see: Zurvan Ex Soar), it is always a pleasant surprise when they are skipped. I have to respectfully disagree with your assumption that having one skill off of cooldown 20% faster is enough to prevent a wipe, and that it should take priority off of optimizing your group as a whole as often as you can. Call me DPS-centric if you want, but this is my opinion.