Why can't Pan go Super Saiyan?
According to this wiki 
pan never did have to go super saiyan mode.


  [...] basically it's because the creator of Dragonball, Akira Toriyama claims that Pan never had a reason or situation to turn super saiyan. Her debut is at the end of dragonball z, as a little kid, and since Dragonball GT is not based off actual manga, Toriyama only envisioned Pan as a little girl in a time of peace, so there would be no reason for her to become super saiyan. Toriyama has also said that he doesnt exactly know how he would draw a female super-saiyan [...]