There are various forms of mobility within the Kingdom Hearts franchise. Mobility changes forms over the course of the games as well as between the games. However, there are themes of acceptable and unacceptable mobility that hold throughout and between the games.
The Heartless travel through dark routes that are somehow connected by keyholes. That they do not disappear from a world when Sora closes the keyhole is suspect. However, that the world must be "connected, tied to the darkness" "闇と繋がった" is important (1)
(Leon explains the keyholes)
(Destiny Islands is connected)
It is assumed that Riku's method of travel where he uses his dark energy and not a 'vessel' '船' somehow links into the Heartless means of travel. This method is continually used throughout the franchise.
Second are those few who simply have strong will. Among these are Sora, Riku and Kairi at the beginning and Beast at the end of the game. This belief/will power induced travel is rare and not replicated throughout the remainder of the franchise. It is used to bring the main characters to a state where they can travel, but is then discarded. In this way it is almost a primal or innocent form of mobility.
(Riku, Sora and Beast travelling on willpower)
Third is Gummi Ship travel, which utilizes technology that came about through the introduction of heartless into the world. That the player fights Heartless ships between the routes indicates either that you travel along the same paths or that they simply are there to cause problems.
The belief form of travel is given important stature an never really looked down upon in any way within the game world. It shows individual power and agency, and especially in the instance of Beast it is seen as something that must be investigated.
The Heartless travel, of connecting worlds to move between, is from the start seen as negative. It comes from the expansion of darkness, but also specifically from Riku's desire to escape his island, to travel. By him inviting darkness and homogeneity he can travel, but it is what is then combatted for the remainder of the game. Mobility is both desired and feared, good and bad, just as are connections. Destiny Islands loses its innocence, but then again, Sora and Riku are able to then save the expansive world through that necessary loss of innocence. Like Japan's entrance to modernity, the opening of the borders and the Meiji restoration, Destiny Islands' path must be read as bittersweet, but necessary.
In the end, the ultimate closing of the door to Kingdom Hearts returns to world to its unconnected, pure state, and in so doing eradicates (momentarily) Gummi Ship travel. However, the emotional links between people are maintained. Hearts and memories are maintained as links between people. Such links, unlike the connections between worlds, are consistently considered good (even in the case of evil characters' links - eg: Axel and Maleficent)
(Leon, Yuffie and Aeris explain the end of mobility and remaining emotional ties)
Chain of Memories
This brings us to the beginning of Chain of Memories. Riku and Mickey are on one side of the giant door in the world of darkness. Mickey finds himself, eventually, in Twilight Town then travels to Castle Oblivion by card. How this happens is unexplained, but such a mystery generally surrounds Mickey's movements. Riku is led to Castle Oblivion by Diz/Ansem instead of giving up/dying. Sora, Donald and Goofy seal the world from the End of the World (non dark) side and end up in some unknown place where they are led to Castle Oblivion by Marluxia (2).
Within Castle Oblivion all action, mobility included, is done through cards. Action cards (magic, attack, summon et cetera) as well as room cards are obtained during battles, but floor cards are different. Floor cards are made from memories of places even if those memories end up being both suspect and partial. Sora's friends don't remember him, he forgets Kairi, but ultimately he remembers (3).
(Action Cards ; Room Cards ; Floor Cards)
While the imperfection but dependance upon memory is interesting my purposes here remain focused on mobility, something that regains focus as one of Sora's final acts in the tower. After defeating Marluxia, and just before agreeing to have his memory restored, Sora seals Marluxia's room in the same manner as he sealed the keyholes in Kingdom Hearts. Thus, the same act of supremacy and liberal agency practiced in Kingdom Hearts is repeated at the end of Chain of Memories: mobility is for those who deserve it, which is to say, for Sora and Company to decide and enact.
(Sora seals Marluxia's room)
Riku's journey is less about mobility and more about liminality between light and dark. However, as his mobility is dependent upon his utilization of the dark, it remains an issue. He comes to terms with his own darkness, his individuality, by taking the middle path between light and dark, social and individual. Riku's mobility is interesting, but it is Mickey's that is important. Originally, he is barred from entrance, however, he eventually overcomes that and manages to arrive to save Riku. His adaptability, Disney's adaptability, while limited, is proved to be unstoppable. The same unstoppability allows Mickey to be everywhere in Kingdom Hearts II. He has absolute and unquestioned mobility beyond any other character.
Kingdom Hearts 2
Initially the only groups that can travel are the Heartless, the Nobodies, Riku through his utilization of darkness and Mickey through his mysterious mobility.
When Sora, Donald and Goofy are given the run down by Yen Sid they are told that the old connections are gone. However, the worlds themselves support the creation of new pathways:
Yen Sid: これこれ、まあ、待ちなさい。そなたたちの活躍のおかげで世界は今元の状態に戻っている。つまり世界をつなぐ道は消えてしまった。
Yen Sid: 心配するな。王が言うには世界はそなたたちに新たな道を用意したようだ。その道はゲートを開くことによって使えるようになるはずだ。ゲートを開く方法はーわたしにはわからん。しかし、ソラのキーブレードが教えてくれるらしい。剣が光を放ったらグミシップに戻るといいだろう。目に見えぬ心のつながりのごとく、離ればなれになっても、全てはつながっておるというわけだ。
Yen Sid: そのとおり。
Yen Sid: しかし気をつけろ。闇に巣くう者たちーノーバディ、ハートレスは闇の回廊と呼ばれる道を使って世界を渡り歩く。その回廊とゲートをつないでしまおうとする動きもあるようだ。
Yen Sid: Now, now. Just a moment. Because of your previous endeavors the worlds have returned to their original states. That means the pathways between them have disappeared.
Donald: How do we get around?
Yen Sid: Do not fear. If what the king suspected proves true the worlds have prepared new pathways along which you may travel. These pathways may be utilized by unlocking special gates. How these gates are opened I'm afraid I do not know. However, the keyblade will serve as your guide. When a beam of light radiates from the keyblade return to the Gummi Ship. Though the worlds may seem far apart and out of reach they nonetheless remain connected by invisible ties. As do our hearts.
Sora: Our hearts are connected.
Yen Sid: That is correct.
Sora: Got it.
Yen Sid: But, be warned. As you proceed the Heartless and the Nobodies will be using their own paths: corridors of darkness to travel from world to world. They may be attempting to link these dark pathways to the gates between the worlds.
Donald: Hey, that's not fair!
These new pathways take the form of commodity connections. One can travel between places as soon as they appropriate commodity is located. Specifically, commodities allow travel from the world to others and not to the world itself. Thus, the order of mobility is that one finds a world's commodity, activates it, and then is granted access to connecting worlds: follow the labour.
(Activating Hollow Bastion's card grants access to the connecting worlds of The Land of Dragons and Beast's Castle)
The only world where this does not in fact take place is the initial trip to Hollow Bastion where it is stated that they feel it's a familiar place: the same heart/memory connections from Chain of Memories justify the initial travel to Hollow Bastion, but not to other places where they've been before such as Atlantica or Agrabah.
(Going to Hollow Bastion from memory)
The end of the game brings about total connection between the worlds that have been granted by the worlds and the key bearers, bringers of foreign influence. However, the only ones to use this mobility are Sora, Riku, Mickey and Company (Diz/Ansem included), and the Moogles, the merchants.
William claimed that Moogles break the 4th wall, and they do. They are also the string that connects all of the games together. They are the merchants and creators. They synthesize/build items and they sell cards.
(Moogles in KH, COM and KH2)
It can only be assumed the franchise will continue as it has been so popular. The logics of sequels and remakes demand no less. What we will of course see are the increase of key bearers (the count is at 10 although 3 of those are the same being, and 3 are 'dead') who are mobile. It will ultimately be a battle between the good key users and the bad ones. It will go directly back to Triton's fears of protectionism and the unavoidable havoc wrought by transnationalism and multinational business. On the one side will be Disney, Sora and Riku (if they do not move to new characters), and on the other can only be some allegorical embodiment of multinational big business turned bad, which of course isn't Disney. No never.
(1) The word 繋ぐ is consistently used in the Japanese. However, it rotates between connected, tied and linked in English.
(2) Mobility of the Nobodies is assumed to be in full functionality between floors of the castle and it is assumed between other worlds although 358/2 Days will likely have more to say about this time.
(3) Memory here is not opposed by oblivion as it seems to be in the naming. Rather all memories are tied to hearts and people and if strong enough are permanent. This is, of course, a rather simple understanding of memory that is slightly more in depth throughout the game, but unimportant for the present purposes.