Fujitora is not as careless as you picture him, give him more credit as an Admiral who understands the necessity of upholding the law. For example, just imagine how angry Fujitora was at Doflamingo, given the chance he would’ve completely annihilated him himself, but he still understood the complexity of the situation and how he as an Admiral needs to solve such matters patiently, that by itself is what paints Fujitora as a badass imo
That’s why I didn’t like how Fujitora randomly freed Mariejois’s slaves without proper explanation of the scenario, we should at least know if the Gorosei were informed, maybe that comes later
But yeah, Fujitora and Akainu are by far the most complex Admirals with a shit ton of lore to come concerning their ideologies and character. There’s nothing Akainu wants more than to purge some pirates but he’s no dumbass, he understands the value of his position as Fleet Admiral and won’t just casually show up to fight while leaving HQ in shambles. He’s fuming now though so I expect him to take action soon lol