Well for some reason, i thought the drop game in Dream drop distance was a improvement cause it was shorter and easier to play, the gummi ship was more fleshed out of a game like a shooter. it was almost like gradius where you can customize the ship with weapons and such. But the gummi ship thing as a whole is unfitting for a rpg game to suddenly have to use it every time you want to visit new worlds. Least you don't need it after you visit the world.
How would you like it if you was playing final fantasy and every time you wanna use the ship to fly, you go into space like a star fox game mode just to get to where you wanna go? That would be very annoying after a while, this is a RPG game after all. Not that mini games are bad in rpg, some are questionable.
Final fantasy 7 has lots of mini games, the thing is, yes they are part of the story some times. But is just a simple game, not a completely new game. You could have just made a separate shooting game from the gummi ship, packaged it as a download title for $10 or something. It has enough effort put into it that it can be is own game that can be played for a few hours. The mini games in final fantasy 7 are just quick 2 minute games you play once during story, the bike game to escape midgar, the strategy battle game to protect fort condor, the snowboard mini game, sub marine mini game, chocobo racing, arena battles, etc. They are just simple games, not repeating game you have to play constantly between the actual game.
Diving mini game is short and simple, even though it happens often, is not as bad as a full scale shooting game inside of the actual game.