In hindsight, Silent Threat would have been a lot more interesting if it pursued a conspiracy angle rather than portraying the GTI as a bunch of angry guys who happened to build a giant destroyer. That doesn't strike me as how an intelligence agency would defect. They wouldn't take things by blunt force - they'd take them through manipulation. Hence, the silent threat. 
They're trying to overthrow not one but two (because the Vasudans aren't going to take this sitting down) governments that are only being held together by the military need to confront an existential threat in the Shivans, who have both been in a state of war for at least a decade and a half at this point, and who have both have their capitals lost or destroyed by a decapitation strike within the last year.
Even if they seize control of the leadership or the capitals through stealth, they can't really expect everyone else to just roll over for them. These are people who have learned the value of decentralized control and commanders operating on their own initiative the hard way, who are primed and ready to take on anything that they perceive as a threat. The first mission of Silent Threat, where you essentially commit mass-murder to preserve the alliance with the Vasudans and not a single pilot in your unit even
blinks, and you as a brand-new transfer to the squadron are totally trusted to go along with this, is illustrative of the level of commitment here.
At some point GTI is going to need their superdestroyer to pull this off, no matter how skillfully they are manipulative.
