Are you regularly playing content so poorly that you need to use Physick or Resurrection? That's the same toolbox argument taken out of context.
If you queued as DPS, you offer extremely low healing capability as summoner or Arcanist, do you feel compelled to help healer with your low-healing capacity? The reason you can heal at all is for solo play, just like the WHM/CNJ's ability to DPS is for solo play.
Those tools exist and aren't locked away because your role should be obvious. They allow those other tools to be used during dungeon play because it doesn't make sense to disable some tools only in the dungeon, and there will be cases where emergent play can happen, because it's no PvP content. PvP content they disable some tools that are unfair, and you can't use them out side of PvP because it sends mixed messages about which skills should be used during dungeon play.
Here's a better analogy. Your pipes are leaking to your shower. Do you
A) Call a plumber, and have them rip apart your wall to fix the pipes, but fixes the pipes correctly, leaving a hole in the wall.
or
B) Call your handyman uncle bob, who rips apart the wall and lacks the tools to actually fix anything , so he duct tapes the leak and duct tapes over the hole in the wall.
Note that A, the plumber only does his job and leaves, leaving either you to solve the problem or call another person to fix the wall. For B, while something of an exaggeration, this comes from experience. For legal reasons the Plumber may not be allowed to fix anything BUT the pipes because their insurance won't cover them if they screw up anything else and you turn around and sue them. For B, Uncle bob doesn't have insurance, and if he screws up you will be paying more to fix the problem correctly.
When you force someone to "do everything", they are not good at everything. Hence the term "A Jack of all trades, Master of none", everyone has something they are good at, but they become miserable when they are forced to.
As for that Sylphie image, that is taken out of context because Sylphie was using her own life force to heal instead of using the natural forces. It has nothing to do with DPS.