If Emma controls the HFC again, then it would open up some cool opportunities. She could lead a new Hellfire Club that works for mutant rights in a more subversive way than what current X-Men are doing.
Think the current X-Men want to run the mutants like it's the DNC and they're stuck in the 90s. Emma would be like Bernie Sanders (or to a more relevant compariso Malcolm X) and go against the polite establishment.
Emma was co-leader when mutants were nearly extinct and they had to take more extreme measures. The current X-Men leaders have the privilege of a full population and can afford to play nice now with the governments and the world. Emma would know that type of system isn't going to work if mutants ever become extinct again. And you could argue that the X-Men's new trust in governments and world leaders isn't sustainable.
I don't think Marvel would want to put Emma in the spotlight like this though nor take the X-Men in this direction with a lot of political nuance, so it's probably best that this book leaves open opportunities for Emma to join the X-Men instead.