really? your theory on polygamy being good for women is logical? even in societies that allowed polygamy it was very rare. It was mostly practiced by a select few that had the resources to provide for many women. The women were status symbols!
from Wiki:
Patterns of occurrence worldwide
According to the 
Ethnographic Atlas Codebook, of the 1231
societies noted, 186 were monogamous. 453 had occasional polygyny, 588
had more frequent polygyny, and 4 had polyandry.
[2]
At the same time, even within societies which allow polygyny, the
actual practice of polygyny occurs relatively rarely. There are
exceptions: in 
Senegal, for example, nearly 47 percent of marriages are multiple.
[8]
To take on more than one wife often requires considerable resources:
this may put polygamy beyond the means of the vast majority of people
within those societies. Such appears the case in many traditional 
Islamic societies, and in 
Imperial China. Within polygynous societies, multiple wives often become a 
status symbol
denoting wealth and power. Similarly, within societies that formally
prohibit polygamy, social opinion may look favorably on persons
maintaining mistresses or engaging in 
serial monogamy