There's nothing wrong with that theme, especially considering that's a hugely common theme in a lot of stuff aimed at the same sort of demographic as Final Fantasy, but it's more a matter of how it's delivered than the theme itself.
For example, the theme of "friendship" in FFIX versus in, say, FFVIII. For me, the theme of friendship in FFIX works better than in a lot of other Final Fantasies for the simple reason that the characters in FFIX are all so different from each other that it actually means something.
In other Final Fantasies, we're told characters are different in that they have some different personality traits, but their overall goal and their reason for entering the conflict is almost always exactly the same, such that it's never in doubt whether they will work together. Like in FFVIII. All your primary characters have the same age and the same background (sort of barring Rinoa), and are all given the same missions and have the same goal. Was it ever in any doubt that they would work together when they have no reason whatsoever to not have the same goals? This is kind of true of other Final Fantasies as well. It has the problem of making them generic. Yeah, they have a personality, but the personality doesn't affect the plot in any way, and it often has a problem of "Oh, they have to feel this way now for X plot reason/power of friendship moral" without any real buildup.
Compare that to FFIX. Everyone's goals and motives are conflicting from the very start. Every single character has a unique reason for joining the adventure, and they often end up being completely at odds with the rest of the party. They have actual character conflict, such that when two characters who used to be enemies actually do become friends, it's meaningful. Characters regularly leave your party to do their own thing, or have to take actions so at odds with their goals that it seems entirely plausible that they might not come back. That makes it all the more powerful when they actually do band together and become a team.
FFIX isn't even the best example of how the power of friendship can be used successfully in games, but I think it is a good example of how much of a difference "show, don't tell" makes in pulling it off.