Harry may give them no choice, I think we are coming to the time the GateKeeper foresaw where Harry challenges the Senior Council (for real) about how they have been acting, executing Warlocks (when Demonreach is available), the actions of the Black Staff in breaking the Laws of Magic, the failure to protect and nurture the magical have nots and most of all the failure to address the Black Council.
The fear was that the White Council would split as Wizards might pick the Black Council as a putative winner, however a Harry based win against the Titan (and the Black Council) will see these fairweather wizards back Harry, as well as the majority of the Wardens and younger wizards, Harry may well have a coalition which can force change. We may also see several members of the Senior Council ‘retired’ in BG, not just the older three in Chicago, but Ancient Mai as well. We may only see a gullible Christos Merlin and GateKeeper left.