The biggest thing that secures equality is economic and political stability, fair distribution of resources, and legal protection. Ie the structures that are attacked as being 'the patriarchy
That made sense until you added that ridiculous sentence about the patriarchy.
Fair distribution of resources is not something that's happening in the patriarchy.
Exhibit A: Prostitution. Prostitution is the effect of a lack of fair distribution of resources.
Very obvious in that the males who have sex with women they aren't attracted to for the money (I hesitate to call it prostitution as the power dynamics are very different and the women may often not know what is going on) are typically from very poor country, and the women who pay them are from very rich countries.
Prostitution therefore, seems the result of a very steep inequality in distribution of resources. It would be interesting to see some study on the prevalence of prostitution and the distribution of wealth in different countries.
An argument could be made that abolishing the patriarchy via a revolution would lead, temporarily, to more male violence - but most feminists I know aren't proposing a typical revolution as solution, anyway. (The only ones who do that are also communists, which might explain it.)
Patriarchy also does not provide any legal protection to women, and as for economic stability ... um, no. Just no. The one country that took steps to ensure economic stability in the future is Iceland, a country that's ... not exactly the most patriarchal country there is.