@Don:
Fujitoras hands are bound because of the system.
Non the less he knows that this system is rotten, that`s why he sees problems in the shichibukai system.
When Luffy beats Doffy, Fujitora could take Doffy without having acted against the WG, but showcasing, what guys are backed up from the WG, who would kill off an whole island to cover up evil plans.
If it will bring the consequences he wishes for is up to debate.
… How is Luffy beating Doffy breaking the supposed bound on Fujitora's hands?
Especially since, as stated by Maynard and Bastille, his hands are not tied to begin with?
Please. Back down for a bit, and look at the whole picture. If Fujitora could intervene, why would he not? And what would defeat of Doffy change that would allow for said intervention?
--- Update From New Post Merge ---
@parklane21:
I think the reason for Fujitora's inaction is because of his rather difficult position being a marine admiral. If he goes after Doflamingo, it will look like he's allying himself with those actively seeking his defeat, which includes a bunch of pirates and revolutionaries. So he just gamble the fate of everyone on Luffy for the moment, which I think is a strategical move. Something like this is probably going on his head: In any case the pirates fail, he is still there and can definitely take care of things, in the extreme.
Then he will not take care of him afterwards, surely. Because that would have been exactly at what you have just described.
Also: Why not go after all of them?