KH3 had its flaws...but I think some people are just way too hard on the game.
One of the complaints I see about KH3 frequently is about how nothing happens until the end of the game. Um, did we forget about KH2, where literally nothing of importance happens unless you're at the very beginning, middle or end of the game? KH2 had the WORST Disney worlds of the three main games. It's honestly not even up for debate. And honestly, neither KH3 nor even KH1 did a great job "integrating" the Disney worlds into the overall story, but at least 1 and 3 made an effort.
Here's the thing: I really don't think Disney was going to go for their properties being overly involved with the original characters/main plot. Even in KH1, which had probably the best integration, the Disney villains were all interacting with each other, other Disney characters and Sora/Riku (and kind of Kairi). We saw in KH3 just how limited Square/Nomura was with the Disney properties. I think they did the best they could with it given the obvious restrictions, and honestly, I don't know how I would've done it differently. For plot reasons, we can't have the Organization getting defeated until the end of the game (Keyblade War) and we've reached a point where the Disney villains who aren't Maleficent or Hades are very underwhelming to SDG and therefore the player. Why do you think Mother Gothel and Hans had to become Heartless?
KH3 easily could've just taken the plot of the movies for each world and called it good, but (for the most part) they didn't. They at least made an effort, and a darn good one. Vanitas in Monstropolis was done really really well; he was literally resurrected from the negative emotions the world was producing. What more did you want? Marluxia had the flower theme and interactions with Mother Gothel, Luxord had the prior connection in The Caribbean. Was it done perfectly? No, but I think it was done really well still. Certainly better than any other game in the series, barring KH1.
I used to be in the boat of, "let's rescue Aqua and Ventus earlier!" but here's the thing. Once they were rescued, we would literally have no reason to care about the Disney worlds anymore. We would rush through them just to get to main plot stuff. We do the same thing in KH2, but at least in KH3 the Disney worlds are well done and fun to explore. There just wasn't a good way to do anything before the end of the game while still making sure the player cared about the Disney stuff.
Not to mention, we did get cutscenes after each Disney world filling us in on what was going on. That's a hell of a lot more than KH2 or even KH1 does. KH1 isn't perfect in this regard either; you can literally skip Olympus, Atlantica, Monstro, or Halloween Town and you will miss nothing of importance. The game will literally just go on.
So, tl;dr the Disney worlds and overall plot were done as well as can be expected in KH3, and some people just need to lower their expectations.