I will not be participating this year, (mainly due to lack of experience) so I’m not sure if my opinion counts for anything in this matter, but I’ll give it anyway.
I think everyone should be limited to the same choices of music, it keeps people on even ground. In my mind it would be ideal to have just a song library that is unknown by the competitors until the day of, it keeps them from planning ahead of time based on their song (like what kind of theme they’re going for, what story they want to tell) before the contest starts.
However I also understand what you’re saying about music being a reflection of your personality, so I do understand the need to have access to your own music, so I have an idea, that I feel is fair. Any of your own music that can be used by you during the competition must be declared before/at the start of the contest. And you must be willing, and able, to share that music with other members of the contest if they ask you for it. The folks who brought the music still have a slight advantage because they may already have some plans for it, yet everyone still has access to all the same music.