This is a pretty good analogy. You could start watching "Stranger Things" from season 3, and you'd figure everything out well enough to follow the story, but the character interactions would be much less meaningful and you'd miss out on a lot of background details that make the setting richer.
Playing the game, it was clear to me that they didn't have the whole story mapped out in detail from day one. Minor plot threads get dropped and some of the lore isn't 100% consistent. But that's also true of a lot of TV shows with continuing storylines. On the whole, the game does an impressive job tying a decade's worth of expansions together into a single coherent storyline where each part builds on what came before. It's definitely too much of a slow burn in the beginning, but the setup eventually pays off and it's one of my favorite stories in all of gaming. Skipping to the last chapter would rob it of a lot of its impact.
When would you say that story really picks up? I played about half of the first expansion and so far it feels like typical anime craziness plot (not a bad thing, but makes it hard to see how the diffent threads interact).
You'll start to get hints of it later in Heavensward, but I'd say the second expansion (Stormblood) is where you start to really get a strong sense that the story has a destination in mind, and especially that the recurring villains have a more specific motivation than "serve the dark god."
The next expansion (Shadowbringers) starts off feeling like an unrelated side story, but then you realize that it's actually tying together some of the seemingly unrelated plot threads from earlier in the game by showing you a different perspective on the lore and some of the characters.
The last current expansion (Endwalker) is where you have to address the reason the villains have been doing what they've been doing, and it ties a lot of things together including the part of the story you're on right now. Without spoiling any details, suffice to say that Ishgard isn't the only nation that has a history with dragons.
There's always going to be a certain amount of anime craziness, but the big picture does come together much more than is apparent from where you are in the story right now.