I think character switching comes down to difficulty of the worlds and improving/advancing the RPG elements of the game. The fact that Sora is the best at everything will probably kill the idea of character switching. I think that if they adjusted Sora to be an all-rounder (with access to summons and whatever other gimmick they want to give him in that game), then give Riku and Kairi (or whoever are his companions) character specific abilities that will make the player inclined to switch it up. Riku will be more dark abilities and speed, while Kairi will be light abilities and defensive/healing. They could even have Xion have the ability to copy others (like if she activates the ability, she targets a heartless and gains that elemental power for a limited time) and Roxas can have dual-wielding focused gameplay and the pillars of light.
You bring up a great point with Sora. He can do virtually anything so switching to another character might not seem ideal.
So, are we just going to ignore Days and 3D? Because both Roxas (and by extension, Xion) and, more importantly, Riku in 3D were all rounders in the same sense as Sora.
Sure, Riku was a tad more offensive, but I did not feel like those two were as different as, say, Terra to Aqua in BBS, lol.
Roxas not having access to summons felt more like a limitation of the DS (considering ReCom also doesn't feature those, even if it's also "Sora"), and Riku also had his Dream Eaters.
Sora is only really an all rounder in gameplay alone because that's how the gameplay was designed to be, in terms of story it's never stated that he's a better mage than Donald or a better knight than Goofy. I mean, Donald can do Zettaflare, even if the whole scene felt more like a meme. lol
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It depends on what game we are talking about. If we go by the end of Re:Mind and assume the next game would be about finding Sora, and the main characters ended up being Kairi, Riku and Roxas, for example.
I'd use a similar approach to the Megaman X series post X5: the three of them are in contact and working together, but they're splitting up to cover more ground. Depending on what character entered the world, you would be treated to slightly different versions of the cutscenes, but you would be locked to that character until you finished the story. Then, after the world's story is done, you could enter the world with another character to explore and collect itens with their own unique abilities, similar to how each character in BBS had a unique explorable trait acquired in Neverland.
There would also be special dialogue by the npcs of that world talking about the character who helped them with slightly different reactions by our playable character. For example:
One of the worlds would feature a scene where the character sets the town on fire. If you were playing with Kairi, she would conjure powerful Ice/Water magic to put the fire off. If you were using Roxas, he would instruct the companions to move the town to put the fire off while he wards off a barrage of enemies, while if you were Riku he would break some sort of dam or water container that would rinse off the fire.
Then, when revisiting the world with Kairi after finishing it with Riku, the npcs would talk about the exploit and she would comment on his quick thinking.
Also, those slight deviations could offer different rewards; Riku's would reveal some secret area with treasures where the dam was, Kairi's magic would leave the villagers impressed and they would reward her with an item, while Roxas's communication would leave the kids in town wanting to be a hero like him and they would grant him access to his hideout with a unique treasure.
Some special worlds would have you using specific characters asked by the game in a specific order and then you would get more than one at once in your party being able to switch them using a command, as those worlds are where the chunk of the story is and need to have some sort of canon linearity to them.
The result would be somewhat of a shorter game in terms of story but with big replay value, with multiple playthroughs needed to collect and see everything, and the world size doesnt need to shrink back from KH3's patterns just because the story parts are fewer.
Other characters like Lea, Isa, Xion and Naminé would provide assistance by serving as our main npcs throughout the story guiding us and offering help, as well as serving as party members in the "locked" story sessions.
The rewards for clearing the game multiple times could be Xion, Naminé and Aqua skins for Kairi, Terra, Isa and Lea for Riku, Sora and Ventus (in his drive form with the multiple swords of light, or maybe using Vanitas' Void Gear for his second Keyblade since he theorically should be able to dual wield as Vanitas is another heart within his own) for Roxas, etc.
They would play exactly the same as the original trio of protagonists, just changing the voices and some animations as well as the keyblades to match the new characters.