I am late to the party.
Commodore Stone is made out to be evil, upstream. He wasn't going to ignore Kirk's actions. Discipline him, but quietly. Just no trial. Every other captain would still be served notice - screw up and lose your command.
Loyalty is less valued nowadays (at least in how many people talk) than strict adherence to policies (i.e., have the court martial). But, loyalty is very important.
2. Kirk and the PD are fleshed out in other threads, and if I recall, it is always or almost always a) to undo someone else's damage (Gill) or because the Ent is threatened (Apple, Armageddon). He tampers with Sandoval and Leila's Paradise, but that is a Fed colony, not an independent pre-warp culture. Just sticking up for my favorite hero.