Women should be required to cover up. Their tits are a vital part of their sexual organs, unlike men. A woman who walks around with her shirt off should be arrested. The analogy to open carrying is a bit out there. By the way, I'm heterosexual. I would not like to see the vast majority of women with their tops off. It wouldn't be like walking around the Playboy mansion, guys.
Being topless or even nude would not really be much different than what women often walk around in nowadays anyway. And you're right, the majority of women are not models, and many of them would be considered unattractive to the point where them being nude in public would be an eyesore.
To this, I counter that it's the same with men, and Joe 6-rolls who weighs 400lbs does not have to wear a shirt, despite being an eyesore.
Frankly, as far as toplessness for women goes, I'm all for it. I would imagine that well-endowed ladies might find it uncomfortable, especially while jogging or doing other strenuous activity (the sports bra was invented for a reason). And keep in mind that most businesses already have a "no shoes, no shirt, no service" policy, which would not change.
As for the parallels between open carry and toplessness, the
logic is roughly similar in the vein of personal liberty (it's not hurting anyone, therefore why should it be banned?). The difference in lawfulness extends back to antiquity and English common law as well as traditional christian values, which demonized the exposure of women in public. Keep in mind this was also back when women were considered little more than possessions of their fathers or husbands. I contend that it is a mere throwback from that period, which just never went away.