We don't just model ourselves to attract a mate. Men often wish to appear more masculine so as to intimidate other men, for example. This effect is absent from most discussions about preferences and self-image.
Obviously not every schoolyard bully gets an army and a navy to play with, but they're all dangerous in their own ways, and that danger often stems from a self-conscious desire to project power.
Putin's propaganda features these absurd strongman displays of masculinity because it works, it's a very well known and ancient exploit in the human mind and societies as a whole.
I'm sure Putin would prefer to do the evil things he does without having to do the whole song and dance of propaganda.
Unless you’re talking poisoners and embezzlers and the like who don’t need to warn because they don’t engage in direct conflict.
I get you; someone can look helpless but be packing a Desert Eagle .50 and prepared to use it in any trouble. I don’t see how that is an advantage over not looking helpless, unless the idea is to attract trouble and then kill it.