The World Would Be A Better Place, If Women Needed Sex More Than Men.

Why do you think such is the case?  Please elaborate.

Not necessarily so.

In terms of assault (sexual assault is that to which you refer, I trust) those acts are not acts of sex.  Rather, they are acts of violence.  They would still be unlawful.  Prostitution?  As long as there is a demand, there will be those who provide the supply, so there will be prostitution, regardless.  Harassment will still take place, because it, too, is not an issue of sex, but one of power.  Control freaks would continue to delight in such acts, regardless.

So, those things considered, the world would likely not change much.  If anything, it would simply change the dynamic of power in those aspect from males to females.  No gain, no loss.