Maya, Quinn, Lilly, they would be all Bad leaders of the Hots, for different reasons. While Josy desperatly need her own content, and I mean as a personal storyline for her, what is about her. We dont know her goals her motivations , what she want to achieve etc etc. Every main girl has their own story, Josy however Share everything with Maya. If Maya end up joining the HOTS. that would be an another story that she would share with Joey, I'm not sure how I feel about this as of it right now.
With all that said, right now I don't see Josy as someone who is fit for a fight for the Presidency, I don't see her entering the power play, the Hots Civil War what is about to begin.
If I have to pick someone, I would Say Elena would be a great president for the Hots.