Did you miss the part where she sort of got kicked out of the X-Men? Sunspot isn’t part of the X-Men, Xavier is dead, Warren doesn’t even own his company anymore. So far, has she been portrayed as anything but a fighter for mutantkind while she’s been at the head of the HFC? She’s already built schools for mutant kids, which was her entire purpose in this role. What you’re describing hasn’t happened and won’t happen. The whole reason she’s there is to help mutant kids and that’s what she’s been doing.
Callahan was able to take down Havok, Karma and her New Mutants. Could the X-Men find them? If he really wanted to take down Emma, he probably would’ve had something planned out. Emma not getting captured would’ve only delayed the inevitable.