I suspect a lot of "evil admirals" were promoted by votes from, or just to appease, reactionary political movements.

Yeah kinda. In politics there's going to be scenarios someone has to choose between doing the right thing or doing what's best for their career. And yeah, militaries have politics at the top, just not the left-right politics that's common in a democracy. These political scenarios filter out the "do the right thing" people and prevent them from advancing to the top. Not all of the time, but often enough that there's a higher percentage of shitty people in leadership positions then you'll find in the general population.