Actually I ignored that part of story as complete non-sense It was true only in early medieval aka Iron Age, in late medieval female top-tier rulers are became more or less accepted (obviously we're about Europe). And game is like most fantasy games isn't in Iron Age (pro-tip : windmills!).Women are NOT fit to rule in this society, her father originally wanted her to rule a smaller domain but she was "forced" into a political marriage with the late King.
Biology. I know - it's a heresy in many countries today, but biology is a real and still ignoring every type of propaganda we have. At least we have excuse that it's a fantasy gameAnd Pendragons main issue is that she is not accepted among the males while still being equal or supperior in skills.