WoW is everything opposite of what you said.
It's the reason why I quit that game which I played for nearly 7 years to come here during Heavensward.
In FFXIV, the story is a guide into this new world (as a new player). The quests needed a reason to exist and the MSQ gives it. The world made sense and dungeons didn't exist for the sake of leveling, but existed because it had a reason of being in the first place. Leveling is secondary. In WoW, leveling is primary as a new player the moment you get in game all you are doing is spamming dungeons and nothing more. In FFXIV, there is a questline for each and every class and profession, with rewards that make sense and are appropriate to level for the most part. This enriches the gameplay. Nothing can be said for WoW in this aspect.
Coming here years ago from WoW was admittedly hard. The GCD was longer. The MSQ was something I'd never encountered in an mmo. The profession system kicked my butt. (Switching from saying guild to FC ?!) The constant thought of "point me to the dungeons I need to spam all day long to level" was slowly being eroded, because here in FF I don't need to follow that WoW thought process. I can do ALOT of other things to level or have fun here. Yet everything has a reason in this game because of the MSQ.
I do agree that the MSQ needs work, but to eliminate it or locks acquired through MSQ for new players ? You're asking for a WoW clone.
The things that others are suggesting are game breaking. WoW survived only for so long in my opinion because at its launch and through BC it amassed popularity in the west as the de facto mmo to go to (and the only one). Now there exists other choices. In a recent 'documentary' like video I watched in how Yoshi went along creating the AAR, they studied mmos extensively and why they were successful and why they also failed. I honestly believe that the MSQ is a part of that decision making process in a successful mmo with a large playerbase.