In a system where social welfare of the young, the sick and the elderly was almost solely delivered by women in private homes supported by their marital partner's occupation, and where the rate of stable marriages was in the 92nd percentile, giving women the vote might have brought on today's Fathering-by-Government and cradle-to-grave socialism a lot sooner. Few marriages can survive when intellectual debates over the system itself infect the household. As in the writings of Abigail Adams, women were free to influence their husbands.
The other bad thing about universal enfranchisment is today's "one person, one vote" socialist ideal, which the Founders dreaded. Then, voting was a privilege for those who owned property. In relation to the old system, the wife was "covered" by the head of household. Now, everybody votes, no matter how ill-equipped, and the left is trying even to get convicted felons the vote. People living hand to mouth on drugs get the same vote as people creating jobs for thousands of workers. That's taking democracy too far -- removing all obligation to give back to society.
The problem with the left is that they simply can't envision the complexity of human organization. You can't replace an entire organic system of natural law with an entirely synthetic mishmash of political correctness and expect it to produce organic, sustainable results. The farther societies veer from natural living, the worse things get. Our current reliance on mass systems of water, communications, food, energy and GroupThink are making us vulnerable to overthrow. Communities need to be able to sustain independent and localized resources. That is the essence of Federalism.
Female heads of households had no vote, whether or not they owned property, and a husband’s vote is not a wife’s vote.
Your argument about women voting for socialism is no better than arguing against giving blacks the vote for the same reason. (And, indeed, white women still on average vote conservatively today.)
FR is full of cro magnon types where women are concerned—which hurts the conservative cause.