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.
Perhaps... but the problem is we don't know nearly as much about most of the admirals to make claims one way or another.
Also, I doubt SF captains aren't at least aware of the potential threats out there... they'd be rather ignorant if they were not.
I'd prefer Trek move away from the 'crazy admiral' trope (it never seemed right to me in the first place for an organisation as the UFP - I'd make some allowances for an admiral to be shown as being affected by various events and wanting to do 'something', but desperately looking to do it 'the right way', and otherwise to demonstrate they can rise above that behavior too and remain in line with UFP ideals and principles - SF captains certainly demonstrated it can be done time and again... admirals should too). I think they are doing a good job with VADM Janeway on Prodigy though... I certainly hope it remains that way.
Alternatively, we could also say all admirals who appeared 'somewhat insane' could have been alien infiltrators.
