The Eorzean Alliance needs a standing Ul'dah, not a Ul'dah in ruins. Using force to remove the Monetarists would require open war against Ul'dah which would weaken it tremendously. Further, removal of the Monetarists without the support of the public would leave a huge power and money vacuum. The Monetarists bankroll a lot of Ul'dah's armed forces. To remove them and have any hope of keeping Ul'dah from decending into chaos, the people would need to want the Monetarists overthrown by force. That situation doesn't exist at the moment.

Garlemald is on the cusp of a new invasion, this time fully supported by the emperor. The city states cant waste man power and resources trying to force Ul'dah into a different state against the will of it's people. For the Monetarists to be overthrown, the hearts and minds of the people is the battlefield that needs to be won and that cant be done by brute force and ignoring Ul'dah's laws and sovereignty. Do remember Germany was under occupation for a very long time after the war. That's what usually ends up happening when a foreign power forces a change of ruler.

While they have been secretive about the details of the crimes we are accused of we are wanted fugatives by Ul'dah. The Monetarists have used the law in their favour. Infact they have been very careful to make all their public actions and comments well within the law. We are the law breakers. The fact we are certain not to get a fair trial means that our actions make sense but from a legal perspective, they have covered their bases and played us very well.