Ok, random TTRPG thought: in a lot of instances, players and GMs seem to treat Intimidation as an overtly hostile act that almost by nature involves threats and failure to Intimidate leads to combat. I think that leads to it being underused since Persuasion or even Deception aren't as "risky."
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I've also used intimidation for very attractive characters in similar ways.
Knowing someone has power can cause intimidation. A simple crush can cause you to be intimidated!
It really matters what the players are doing intimation wise too. But often I see it as no different than deception in terms of riskiness, combat possible but not the only fail state.
You're right failure mode of intimidate/coercion doesn't always have to lead to a fight and probably shouldn't.
“You ARE the Brute Squad.”