because she didn't like her basketball coach. Because hello, she is aware of her freedom and if she just wanted to transfer she could have transferred to a different school already and being playing at another university already.

Going on a mission seems like a decision that matches her character traits of being intensely devoted to whatever she puts her mind to do.

I am not saying she couldn't transfer when she returns, but the mission choice is certainly a whole separate thing than any transfer decision would be.