In my opinion, suffrage was not the mistake. Granting the vote to women in and of itself would not have impacted society any more than it had when former slaves gained the franchise after the Civil War.
The problem arises after Eugene Debs and Victor Berger and the other socialists in the labor movement co-opted the Suffragettes in 1914 or so and twisted the agenda.
The Suffrage movement coincided with the marxist labor movement, the Marxists also wanted unuversal franchise but for very different reasons.
One of the foundational principals of the Marxist labor movement was the abolition of marriage and the institutionalism of child rearing by the state. In those early days America would not tolerate such dictatorial concepts and met the Socialist labor movement with batons and bullets.
Debs, Berger and others in the Marxist cadre saw the Suffragettes far kinder treatment and realized that they were the key to surviving as a viable movement. The rest is history.
True. Democracy is the tyranny of the many. America has never had true democracy though. America was a Republic, the most equitable form of government for the most people. Sadly, our republic has been quietly delegated into a bureaucratic oligarchy.