Archaeologist here rather than historian, but since archaeologists are anthropologists and kinship systems are definitely something we study so I hope its okay I am answering. You might be able to get more examples of polyandrous cultures on r/askanthropology.

There are a few known cultures were polyandry is (or was) the more common practice. The most famous of these is probably the fraternal polyandry system in the mountains of Nepal. In this case, a woman would marry multiple brothers. It is thought this practice developed to help keep resources within the family because land was so precious in the Himalayas and also helps control population growth in a place resources are limited. It is dying out as the region is modernizing and subsistence practices are changing. Link to article about this practice.

As for why polygyny is more common, from what I understand it is essentially due to the fact that women are the ones who become pregnant. This is tied up in a lot more complicated social factors that of course vary across cultures, including that in patriarchal societies polygyny is a way for powerful men to maintain control over women and lesser men and that men formed the armies and there were times when men were killed off at a much higher rate than women.

Essentially, polyandry, polygyny, and monogamy are all at the core about control over resources and power, but are just shaped by various cultural and environmental factors such as subsistence strategies, economies, predominance of warfare, and religion. Just in most places, it is beneficial for women to be having as many children as possible, in which case polyandry is not the most useful system and polygyny or monogamy are.