I really feel that the OP's point is precisely what is making me hate Dawntrail's MSQ.
Usually it was less egregious in ShB or even Endwalker, because the story there was much more dynamic and better paced, but in Dawntrail you potentialize how bad this design is because of the very nature of the story being told.
For example (Zone 3 spoilers)
There's the trial that requires you to cook, and all that you can actually do is just chatting with locals and fetching things.
What should've happened is an actual minigame involving cooking in which you control Wuk Lamat (so to avoid conflicts with the WoL potentially being a CUL). There you have it, suddenly something that adds a ton of dynamics to the challenge.
I absolutely hate to compare XIV with WoW (which I don't even play anymore) but there they know how to make the questing experience more interesting even for common quests. A good example is the kill quests.
WoW: You interact in a more dynamic way with the environment, being able to pull a lot of enemies to see how far you can handle and finish a quest more efficiently. Stronger mobs can count more heavily towards the completion in some cases (World Quests), etc.
XIV: You're asked to clear a road from threats. There's 2 or 3 "purple smoke markers" that spawn a couple of enemies that will die in 2 or 3 GCDs... and there is. Almost an 'instanced' experience. And funny because you actually have interesting 'kill quests' right around the corner, and they ironically are FATEs.
In the end, I absolutely don't want XIV to become WoW, but there are some hints that could serve as inspiration for a better player experience.