I feel as if you might not have played the other Final Fantasy MMO either
Speedruns, or "Sac" pulling is a "norm" in the realm of FF MMO's. Now I agree with you that skipping everything is a little questionable, but how about they give us a reason to kill the trash mobs, not just using "time" as a reason.
For instance, make them drop gil (very small increments), items to turn in for gear (nothing great, maybe?) or atleast a little incentive to spend the minute or so to kill them. Otherwise people are just going to speed past them
If you did play FFXI, take Dynamis, or Limbus for example. Trash mobs dropped pieces of currency, or just random objects that at the bare minimum put something in your loot pool.