I may be going off topic a bit here but myahh, anyway u dont seem to understand the character of fujitora nor his intentions as a marine admiral.
U are messing things again, a citation as to someones name, title, or even the work someone does is something u take literally, but not the words spouted by characters around, fujitora had his eye set on doflamingo from the start:
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But as doflamingo said, fuji does not have anything to prove but just wild accusations and nor does he have the authority to do anything to doflamingo as of now.
Even when he got the call from sakazuki that the doflamingo leaving the shichi was just a false report and even the panel im gonna show, its where fujitora gets a glimpse of the authority and power doflamingo hold inside the WG.
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First here we get the real reason fuji really joined the marines and what he intends to do on dressrosa too, fujitoras main objective as a marine admiral is the abolition of the shichi system, he sees the shichi as nothing more than people who misuse the amnesty granted by the WG for destroying and hijacking countrys an such, as he mentions the case of crocodile too, he even threatens dofla that if the system comes to be destroyed than the price on dofla would rise and he would get hunted down, but seeing how dofla still got the authority as a former CD who has the power to call upon forth the CP0, who are in direct order from the CD's and still in power as a shichi then fuji has nothing on dofla and he tells him how fuji is going to be corrupted himself on turning an blind eye on every dirty shit doflamingo does during the time being, but he tells that just for now, as even dofla says " Kill me while u can ".
Here goes down ur theory of thinking that fujitorais a guy who never does dirty works or other things, he actually ignores anything that will happen to the country be it killing or anything by turning a blind eye on everything because that's what he got ordered to do by his higher ups.
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Here maynard thinks that doflamingo should be stripped of his title and be arrested by the marines, but fujitora sticks to his main plan of destroying the whole shichi system and not just arresting one or two, which would result in another shichibukai who would abuse again the title, the only way to stop these things done by certain pirates is to destroy the whole shichi system and then there would be no abuse of countrys throughout the world, this is actually the meaning of fujitora's quote to maynard, that he even compares world government, an orgaization who tries to play the role of god, which is completely the opposite of it, as even the citizens itself are filled with rage because of the high corruption of the WG.
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Even here Sabo tells fujitora that he is acting oblivious and is plotting something and intends to make fujitora act serious and fight seriously during their fight and not fool around ( Here we see an beaten up Sabo with scratches and bruises all over his body while showing Sabo huffing around at a non-serious fuji who came to this fight to use it as an excuse of not helping the hateful doflamingo).
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1. He despises the shichi and its his main reason for becoming a marine, he doesnt help luffy because here on this scan u can see that fujitora thinks that marines cannot be heroes on this island and that fuji somehow breaks his promise of helping doflamingo and breaks the law of marines of helping a CD, but instead he leave it in the mercy of pirates, seeing at as a dangerous move Sabo asks fuji what is someone knew hsi real motive Issho calls it a gamble and goes to the royal plateu and places his bet on luffy, a rogue who has all the rights to crush an shichi and a CD in behalf of issho.
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If Fujitora ever had the authority to attack doflamingo than he would crush him into oblivion, if fuji was someone who acts on his own whim like sakazuki than we would have a roasted flamingo stew tonight, but the guy rather stays true to his intentions, and let a pirate to crush doflamingo and his regime.