Not sure if a chicken-out-rule is really needed or beneficial for the game as there a lot of mechanics around a throwdown. For example getting heat for bringing guns, there is hassle card that gives you money for every injured dude, you would also make the Grim Bastards ability in pile-ups useless etc.
Personally I would not suggest to change this or house-rule this but of course - it's your game :-)
You know what? I think you've convinced me. Plus, as the previous poster noted, you could always bribe your way out of a throwdown.