i think the reason why it is like this is because for example in VII it is clouds story and he is the main character therefore he is present in all battles as he is the main person that the other characters offer to join along on his journey to help out and save the world alongside him.
On X its a different concept as even tho tidus is the main character its not exactly his story he is present to join the guardians for yuna. therefore he is not the main person who people have joined so he is able to be removed from the group as he is equal to the other characters.
In XII vaan isnt the person who the story is directly about either, the group is formed from different people offering to join and help out and was not formed directly by vaan therefore different characters can be kept in and taken out of battle.