The only way in which the game's design "encourages" people to see the story as the most important part of the experience is by making it mandatory to complete to access a lot of the other content.
In all honesty, if the story didn't exist the game would probably be fine. There is a rock solid MMORPG with heaps of content to be played, and MMORPGs were popular long before anyone put stories in them. I personally don't really care for stories in MMORPGs because I'm a roleplayer. I don't get all that much out of the game building up my character as the chosen one for hundreds of hours when I can't actually ever reference those experiences in RP. All characters go through the exact same story so it doesn't make any sense to claim those experiences as uniquely yours while in character.
So, from the perspective of someone who is really into crafting their own narrative and participating in bringing the world to life, having one linear story for every character in the game is actually a significant step down from having a system that chronicles a unique path through life for your character.
I don't mind if people like the story, but the idea that the story somehow makes this game is in my opinion simply not true. There is likely a strong bias in the community to really love the story because if you don't like the story the game drives you away with its insistence that you play the story anyways. The issue is that there is simply no need for that. The people who love the story wouldn't somehow miss out on anything if the people who don't love the story weren't forced to sit through it.
I think the story is OK and I want to see it play out, but it isn't my main reason to play. The story only dominates the play experience of FF14 because it insists on itself to the point where you have to literally pay money to not play it. I don't think that does this game any favors.