I don't think there are many women who'd feel threatened at the prospect of receiving fewer unsolicited dick picks from the sort of guys who view them as interchangeable with robots, and I'm not really sure what more impact on 'the current balance of the sexes' you'd expect to come out of something like that.

I am not sure what are the proper words to explain this in a polite company, but women have been policing sexuality since ever. Men are typically jealous of their own partners, but they don't care much about what strangers are doing. Women pay attention to each other, and call out "sluts", because they do not want sex to get too cheap, as that would threaten their own negotiating power at the dating market place. Robots could be the ultimate "sluts".

How much sexual power each woman has, that is highly individual. Some women are more attractive than others. Some women have many other qualities, but for some this is the greatest leverage they have. Therefore, if that power suddenly dropped to zero, because of abundance of cheap robotic sex, different women would be impacted differently. Some of them might be even happy about it, as you suggest.

But it seems that many women are concerned, because when similar topics are discussed in the news, there if often women who insist on policing male sexuality. Sometimes, like when discussing prostitution, porn, or just too much free sex, this is done under the pretext of protecting the exploited women. And yes, there is also that aspect. But when the debate moves to e.g. computer-generated porn, where there are absolutely no real women involved... still, some women are concerned about that, too. This article was about robots, and - quite predictably - some woman was publicly concerned about that, too. So it seems like worrying about the exploited women is not the full story here, because the problem remains even if there are no real women involved.

As a contrast, imagine the discussion instead being about slavery (in a parallel reality when Confederation won the war). Someone would ask "what if in future the robotic slaves will replace the labor of black slaves?". Probably everyone who opposes slavery would say: "great, the sooner that happens, the better!" If we care about humans, then the same thing happening to robots instead of humans is an improvement. But when we talk about how male sexuality is somehow inconvenient for women, when someone says "what about robotic sex instead", the response is always "nope, that would be problematic, too." Which suggests that the problematic part is not about what happens to women, but about what men are allowed to do (even to objects).