Everyone talks about how they wanted the Enterprise B or C or at least an Excelsior or Ambassador class ship showing up to save the day, in a sort of "call in the cavalry to finish this up" sort of way. But really, wouldn't that completely defeat the purpose of Section 31 being clandestine? They're meant to be the ones who save the day in the shadows while the rest of Starfleet and indeed the Federation continue on in blissful ignorance. They're not doing that if they bring in one of Starfleet's capital ships (especially not if it's the flagship) as their backup.