The Dive to the Heart tutorial in KH1 really embodies KH in top form: fantastic yet imposing, compelling in its dream-like (sometimes nightmarish) execution and sense of scale, full of layered imagery and symbolism which makes more sense as the game progresses; all intended to set the theme of the story and advance the big questions central to the player's journey. KH2, on the other hand, uses a character-centric piece with a good deal more plot involvement to convey information as to what the game is "about." It was a surprise and a nice change of pace, and I've always enjoyed the Roxas tutorial as a great way to shift perspective and expand the narrative beyond Sora's personal agenda.
Like you, I'm not fond of Nomura's apparent plan to thrust KH3 right into the action, especially if that means using Olympus as a launching point. Disney worlds by their nature have something of a predetermined structure: Sora arrives, Heartless show up, Sora beats them and flies away in the Gummi Ship. It doesn't lend to the sense of intrigue (the "hook") a good story ought to start with. It recalls the abrupt start to DDD, which felt a lot like just another episode in a long-running game franchise fans have spent too much money on. But that was also structurally relevant to the story DDD was trying to tell, and while I disliked it I can understand the intention.
KH3 is a big title, though: it has a lot of ground to cover and it needs to take the time to establish its premise and the people central to it so that it can efficiently move its plot along without pausing to reconcile past information with current. A self-contained level, like the Dive to the Heart, an original world or say Merlin's time chamber, is useful for this purpose because the rules are generally different there. One can invoke a sense of danger there which may not be convincing in "generic Disney world plot #n" and use ominous text voices or scrambled plot threads to investigate the story's plan and give the player something to sink their teeth into. That's what it's really all about: whether I'm reading a book or playing a game or watching a movie, I like having a chance to get to know my story and the people who inhabit it. We may have a summary knowledge of what KH3 is about and who its protagonists and antagonists are, but we don't (I hope) know why any of it matters yet. KH3's gotta have purpose and it's gotta convince me to care about it. It's not just another episode.