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This is more a question for Trope Talk than here.
Also, the key world is "often". That reasoning may not be reason for every single Faux Action Girl, but it's something that's a common enough mindset among viewers/writers (or at least used to be) to be worth mentioning.
"It's just a show; I should really just relax"
The Faux Action Girl trope states: "Like the Standard Female Grab Area and Designated Girl Fight, this trope is often caused by writers who want women in their action show, but are unwilling (or not allowed) to show a woman being hit by a man."
But that just doesn't seem like the reason to me, since making your character an Action Girl doesn't necessitate that she get hit by a man (she could defeat opponents whilst dodging their attacks), and the trope has a whole bunch of examples of women who are constantly defeated by men (showing that writers don't necessarily have a problem with the idea of a man beating a women).