Yeah, but:
A) That doesn't always ahppen.
B) That works in the democratic system. Not autoritarian one, like the one presented by WG.
They can simply vanish people if they want, you know? We saw that with Iceburg.
It's not that simple: even in autoritarian states there's often some kind of pretense. Real-world dictators rarely go by "ok look, I want to do that thing and we both know I'm batshit crazy so I'm gonna do it and anyone who disagrees can go die in a hole". More often than not they claim to be fighting terrorists or saboteurs, or to have the good of their people at heart and so on, eventhough their acts prove otherwise.
Back to the world of One Piece, we already know that the WG isn't a monolithic force. The Marine takes orders from the government but doesn't necessarily agree with what they're ordered to do (take Kuzan, for example). For all we know, there may be diverging views within the Gorosei or between Cipher Pol teams. The WG itself answers to the 18 remaining Celestial Dragon houses, but nothing proves that they always speak in a single voice. The WG also probably needs to consult heads of states on a regular basis if only to maintain a semblance of democracy (if not, what are the Reverie summits for ?). So if someone with a loud enough voice raises a valid case against the Warlord System, there's bound to be a couple of ears who'll listen to him.
There's also that vanishing the pacifist mayor of some Grand Line island and vanishing a Marine admiral are entirely different businesses - the admiral is immensely better at fighting back (not that it would stop anyone from trying, though). Besides, Iceburg's troubles where due to the pursuit of a world-class weapon of mass destruction. Who would go that far in order to protect a bunch of privateers, except maybe the privateers themselves ?
Reasoning being that him directly and very openly helping the very warlord he wants to use as an example that the entire system needs to go doesn't give his superiors a chance to shut him up?
That is downright idiotic.
Not to mention untrue. He is allowing them for many major obtrusive arguments against his plans PRECISELY because he does not intervene.
With first being sarcastic "Well, we evidently don't have anyone on the staff capable dealing with Rogue Warlords, so I guess we can't dissolve the system.".
There's more to it than meets the eye. Fujitora told Doflamingo that he would support him. But did he ? He more or less let the Sunny escape, threw an half-hearted swipe at Zorro, met (and probably immediately identified) Luffy twice yet did not really try that hard to hurt him, let himself be stalled by Sabo who admitted almost explicitely that Ishou was going easy on him… Which of these do you call "directly helping" the warlord? Sure, he aided 'mingo in capturing Law, but then in his book that's just helping one warlord down another so it's fair game, plus it's possible that his mind wasn't yet set on a specific plan at that time.
He certainly ordered the VAs not to go after Doflamingo, but I stand by his explaination on this.
As for not being able to deal with 'mingo, he can always argue later that he had his hands full with rev commander Sabo.
Furthermore, by letting the warlord run amok he increases the chance that the case against the shichibukai system could be made by whoever next holds the throne of Dressrosa, giving it added legitimacy.
All in all, I'd say Fujitora is a sly gambling fox in addition to being a formidable fighter...
OR I'm giving it too much thought and it's just sloppy writing on Oda's part. There's been so many turns and twists in this arc that I wouldn't put it past him to have changed his mind a couple of times.