I'm aware that the Mosuo of China are often cited as one of the worlds few remaining matriarchal societies, but is there evidence suggesting that the practice was more common in China? Someone mentioned the naming system suggests this, but is this widely believed? What may have allowed a formerly matriarchal China to turn patriarchal?
I think you might be mixing up "matriarchal" and "matrilineal".
There are a number of ancient texts (e.g. Shāngjūnshū and Báihǔ Tōng, to name just two) that have a line similar to this:
In ancient times, the people knew their mothers but not their fathers
There are multiple references to ancient society being matrilineal, which supports (or alternatively is supported by) the woman radical (女) in the character for "surname" (姓). That is, the family is defined by the women and their offspring, not the men. However this is very much a different thing than a matriarchal society, in which women actually control things. To my knowledge there is absolutely nothing to suggest that women were actually in control in ancient Chinese society.
Compare Jewish society; Men are largely in control of domestic and religious life, but to be considered Jewish you must have a Jewish mother. It's very much patriarchal but still matrilineal.