From what we've seen, being bonkers is a qualification for promotion.
Well, I mean, they treat it like you have to be crazy to want to give up command of a starship. Kirk in Generations is all of that to Picard: "Don't let them promote you." Kirk didn't go crazy but he definitely became more of a jerk.
the incidents involving UFP admirals though are seemingly few though.
Yeah, but they were intense, though that might be as a source of drama.
Commodore Decker: suffered intense loss, so that checks out.
Admiral Jamison: supported a warlord then became obsessed with staying young.
Admiral Kennerly: supplied weapons to the Cardassians. Not sure what his deal was.
Admiral Leyton: paranoia.
Admiral Pressman: unknown. Paranoia perhaps at the Federation and Starfleet being hamstrung by the Romulans.
Admiral Necheyev: ordered genocide. But, against the Borg. Debatable.
Admiral Ross: more distressed and stressed out because of the massive losses from the Dominion War. Plus Section 31.
Admiral Cartwright: just pure hatred.
Admiral Janeway: Well, one she got promoted over Picard quite quickly. Two, yeah, she seemed a little distressed by the alternate timeline.
Admiral Satie: paranoid.
Maybe part of the admirals tendency towards crazy behavior is simply the fact that they get too much information about threats and it drives them crazy from trying to solve it all.