Googling for an answer I learned that at least violence would become almost non-existent and crime, in general, decrease. Those are things that men do.

I doubt it.

Anybody who has any interest in social phenomena knows that society tends to run on its own. Players change but roles remain and the plot. This is true in big and important institutions, in particular, army, large companies ... and criminal organizations, to a degree. I just watched a documentary on El Chapo. A masked criminal said that the state can't win because even when they manage to put somebody in jail somebody else will rise to fill his position.

Much of what causes crime has to do with the social function of crime, producing something customers want. And if that need doesn't go away, it really doesn't matter who fulfills it. In an all-female society it would be women, naturally, women who couldn't rely on anybody else to provide for them.

But they would do it worse, in all likelihood, because fewer women have what it takes to run a big, dangerous, aggressive operation like that.

But what about violence?

Obviously domestic violence would increase because lesbian relationship are more violent and there would a lot more of them. Then again sexual violence as well as stupid macho violence outside homes would probably decrease significantly.

But is there something more general to say about the subject? Hmm, I think that throughout history there has been justified violence (like hunting, self-defense, standing up for the weaker) and non-justified violence (robbery, war of conquest, two drunken losers getting agitated by their poor impulse control). If we leave out wars, which complicate the question unnecessarily, I believe that most violence has been justified or, at least, there has been a strong justifying component. Unjustified violence is usually done by a minority and what "the rest" does has been more or less justified. (I once hit a guy so that he fell off the barstool but let's not go there.)

Anyways, when people say that women aren't violent or wouldn't be in a manless society, they seem to forget this justified violence. So, what they are actually saying is that women aren't able to, say, defend children violently if the need arose. But that's not true, as we all know. What is true is that women don't have to do it when there are men around who do it for them. But if all men were gone...

But those would be a minor issues compared to what could happen to the world in a larger scale. I think that what is true for criminal organizations would be true to some degree for all competitive fields demanding aggressiveness and fearlessness. There just aren't as many women as there are men who have what it takes because of biological reasons. That alone would lead to a economic collapse. And that would lead to unrest. And violence.

But, I have to admit, this is speculation. The deeper idea I'm trying to say is that men serve a crucial purpose in economy. It's not at all clear women could ever replace men totally without making the system far less efficient. Armies, for example, are the same. Women could have armies but they wouldn't be as efficient as men's armies.

Likewise, women have certain traits leading to certain roles men couldn't ever fill and replace as well as women.