Matriarchal are women ruled. Whats being described is matrilinear. Yes, it is more to be desired. Matrilinear societies were common at one time, there is archeological data to support that these people were agricultural based, that in their lives the arts were very important, that all people in the village put their goods into a communal pot and then each took out according to their need. There were no walls around their cities because war was not something they practiced or condoned.
And then the patriarchal tribes came, killed all but the good looking women, and took them off to teach them the "better" way.
I'm not just saying this, there is a LOT of evidence that supports this "When God Was a Woman", also "The Chalice and the Blade" are two sources of information, however there are lots of others.
So, even though this type of society lived in peace, was self sufficient, did not know poverty, had a high respect for the arts, look what we have now, isn't that better?
Sherry