I don't think an overthrow of capitalism is necessary to start implementing these changes.
It's not about overthrowing capitalism. There isn't an intrinsic problem with capitalism so long as it is regulated and harnassed to meet legitimate human needs rather than enfranchising one section society while impoverishing another. A flourishing private sector is a good thing. That is not what exists at the moment. Capitalism is now extractive. The corporate elite, the tech oligarchs, the financiers and the property investors are drawing money out of the real economy and then financialising them into assets - the rate of return on which is actually exceeding growth. In short that means that there are some super rich people at the top and a lot of poor people with insecure work who can barely afford to pay exorbitant rents at the bottom.
You cannot argue that those conditions have nothing to do with a sex industry which is expanding at a massive rate. The internet is the fullest realisation of a deregulated global economic model, and sex, not coincidentally, features prominently in that model. Sex, the lowest common denominator of human nature, sells. This is why advertisers employ it so commonly. And it is also why so many internet capitalists saw sexual services as easy money and became pornographers or delivered other sexual services. And I really think we should extend our definition of prostitution to pornography because it is effectively the same thing in visual form. If anything, it's even more deregulated and abusive.
Now, you can argue that men should not look at porn or use prostitutes (and by way what do you have to say about the increasing numbers of women who use porn? Are they guilt of exploiting these women too?)and you'd be right; but arguments alone are powerless against a vast global industry that, as I have said, interfaces with banks, credit card companies, hotel chains, Google, Facebook, Twitter and even criminal industries - a vast trade in commodified sex with with tendrils everywhere.
Further to that there are the economic conditions that vulnerable women find themselves in. Of course if you created a social democratic utopia then there would still be prostitution, but how on earth is that an argument against not doing something that will significantly reduce it? As well as well the more diffuse patriarchal stuff you mention, women are driven into prostitution by material conditions. There is usually some economic imperative there - whether they're trying to get off the streets, feed their kids, supplement a meagre wage or pay off a student loan. If you remove those imperatives then you might not have eliminated prostitution, but you have reduced it. So why not do that?
You cannot change anything just by advancing arguments. No one ever has. Things can only be changed programmatically.
It seems that many progressives have gone over to the right and are averse to any solution which might mean they have to pay more tax. I find that deeply saddening.