It's not about giving him a leave but Akainu still maintains a very friendly tone with Fujitora even after all his fuck ups, unnatural from an angry boss.
Fuji knows how corrupted the WG is already yet is still fighting for the navy, so knowing a bit more about the past shouldn't really change his stance. If anything I think Fuji's role will be to maintain the navy's reputation and solidarity during the WG collapse in preparation for his future FA role.
What are Fujitora's fuck ups?
- Exposing the World Government, so they wouldn't marines the credit for shit they didn't do?
- Exposing the World Government, in creating the monster known as Doflamingo that terrorized Dressrosa for decade+?
- Abolishing the Warlords a system that prevented the Marines from doing their jobs properly in multiple cases? A decision he made after hearing Smoker out.
Fujitora isn't fighting FOR the Marines (this is what Akainu does). He's fighting for the people as a Marine. There's a big difference in the two. His entire purpose of joining the Marines is related to changing the system quo that's in place.
Fujitora is the most competent admiral Akainu has under him, of course he has to keep it professional with him. Especially when he has loose control over Fujitora in the first. Fujitora's true ambition and goal is still unknown to the readers, we still have 0 idea as to why he decided to the join the Marines. Since the abolishing the warlords came after he was an admiral and had a conversation with Smoker who told him what happened at Alabasta.
The call will likely be tracked by Tensei, I think there’s a big chance the higher ups will eventually know.
I doubt even Fujitora will defect from the navy. Akainu is not dumb, he knows what Fujitora is up to but is still far too lenient with him, he talks shit to the gorosei and even tried to order them around, and he has a sword tattoo on his shoulder, not to mention a potential connection with Dragon. I think seeing his reaction provide some hints on his future role.
- Akainu talks shit to the Gorosei? huh, all he ever did was express anger and told them how the Celestial Dragon's puppets stepped over them... even though Gorosei were the ones who ordered the CP0 to handle the Doflamingo case.. lmao. And then he gets told to shut his "insolent" mouth up.
Those same people are the ones who wanted him as Fleet Admiral over Aokiji. They wouldn't want him as the Fleet Admiral if he wasn't 100% loyal and obedient to them. Mans is the "red DOG" for a reason. He's not gonna bite the hand that fed him.