I'd like to note here that the idea of "paying for things" isn't really that old. While you suggest that men have always provided, that's merely a historical phenomena, partly imposed by our lack of acknowledging many forms of labour that women have typically provided. For example, care work is typically undervalued, but a pillar of our economy. So for the majority of the history of capitalism, women haven't had access to paid work, equal pay, or even voting rights. It's unclear that there is a psychological foundation for an institutionalized patriarchy.