Seems like I missed another of Fujitora action debates.
Anyways, I would just add my thoughts.
Fujitora has all the rights and freedom to defeat and capture Doflamingo. If Tashigi can strip Crocodile of it's title, Fujitora can do the same to Doflamingo based on his actions. As Verus said, even the Vice-Admirals are asking why he isn't capturing Doflamingo.
Despite having all the reasons and power to counter Doflamingo, he still refuses to directly confront Doflamingo or his family. It's not about what he can't do. But rather, what he won't do.
The question, therefore is, Why he doesn't want to attack Doflamingo?
The reason is obviously in his cryptic statements about "World Government being God". He doesn't want the World Government to get the glory they got in Arabasta.
Shichibukai have went rogue in the past. But it's always the Marines who get all the credit for their destruction. So, despite the problem being originated by the World Government's system, they are hardly accused of anything because they themselves stop it before too much happens. And then cover up most details.
This time, People are actually seeing who the true saviours are. If Fujitora had intervened in the fight, hardly anyone would have been aware of Straw Hats' existence on the Island, let alone their role in fighting Doflamingo.
Fujitora is a Gambler. Just like how Aokiji has "Lazy Justice", Akainu has "Absolute justice" and Kizaru has "Unclear Justice", Fujitora has "Risky Justice" or something along that line.
He is currently betting on Luffy to save the day, so as to completely foil any and all plans of World Government to take all the credit for saving the Island from Doflamingo.
This obviously is a risky choice considering the strength of Doflamingo and how it would have been much easier if Fujitora himself had taken actions.
But as said before, Fujitora is a Gambler. He is willing to take a little risk in order to reap the benefits, i.e. abolishment of the Shichibukai.
–- Update From New Post Merge ---
@RomanceDawn:
Oh and Lafitte is Brook's opponent all the way. Their abilities just match up to well.
- Flyer VS guy who jumps high, runs up walls and across water.
- Cane VS Cane Sword
- hypnotism/magic VS hypnotism/magic
- The musical theme they have going.
Yeah, I never understood Nami vs Lafitte.
I can see why swordsmen or snipers would fight each other, or even Captains because they are the most powerful of the bunch. But navigators?
Why would Navigators match up against each other anyway? Especially when Nami always fights females.
Also, Lafitte had Angel Wings, while Brook is Devil from Hell.