There did not used to be a fantasia reward from this quest when I started the game and instead the reward came from being subscribed for a certain amount of time. I was extremely careful before using it because I was aware one wrong click could waste it. I rehearsed my changes on the character creation screen first.

If I had wasted it, I'm not normally someone who buys off the shop but eventually I would have saved up enough if I really wanted it. We should be thankful we even have the freedom to change our appearance at all. We didn't used to.

If it's such a problem to buy it and your character is still relatively new, you could just make a new character and skip cut scenes up to where you were.