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Narf by a real girl do you perhaps mean an unstable berserk unable to control her bloodlust nor willing and searching for something that man has and likely stabbing him in the back when she gets it? For, if we do get real ,a girl able to fight is either a backstabbing rogue who's in it for money, an aforementioned slave (the safest choice) or some kind of a knight who's most definitely unable to join the party due to heavy allegiances of noble lineage or army service.
Or, you know, a heavy athlete who you would hesitate to ever call a woman due to her biceps size of your head and little to no sexual characterisics nor appeal. This last one would only sell as comical relief, and not due to double standards, but due to one and only biological standard.
P.S. There's also one type that doesn't fall into all others: a normal girl type. It's only pro would be stamina and cons would be total unsuitability for combat, since you cannot stay normal in that kind of a job, especially without the amygdala upgrade encoded in Y chromosome (yes, there's a whole war/hunt-oriented overhaul patch in there), a very likely unwillingness to fight strong monsters which any cheater gets to fight pretty soon, as his growth is always faster, and need to be babysit, which makes her almost the same in position as a slave, but with questionable as heck motives, considering the above. SO the final con in case she sticks with the protagonist would be complete and utter insanity and stalking the protagonist.