There's no weird fetish, it's just your thing.
And sorry, I don't remember any game when I got an option to change the haircut "at will".
Speaking of transformation, there's
Interns of Ecstasy Island where the hair grows, but I haven't played it for a while (1+ year) and I don't know if you can choose to cut them now.
If there's any game that implement this feature, there's a few chances that you'll see it in 3DCG games. I think it's way easier to implement it with 2DCG. Maybe you can search or ask in thread with theses filters for a start : 2DCG, Female protagonist, (other minor fetishs or things you like), Renpy/RPGM, Not abandonned.
