Trapped in Vagina

I am currently in a part of the world in which women cover. You see these unrecognizable blobs of black and wonder how anyone can tell who they are or what they are. How the hell do their kids know which one is their mom?
In this culture, women supposedly cover like that to prevent being seen as sex objects, and out of decency. Nevertheless, you see these women constantly harassed on ths streets by men of all ages and often groped and sexually attacked. And something I noticed is that the more covered up a woman is, the more harrassed she is. So how is this cover NOT making her a sexual object?
My theory is that in any patriarchal society, a woman , no matter how much she covers and tries to hide her womanhood, is automatically seen not as a whole being, but as her reproductive organ. Women are not seen as people with brains that create and hands that make, but as vaginas that exist for sex and reproduction.
Therefore, anything that makes a woman recognizable as a woman will therefore make her seen as a sexual object. Can a woman really hide being a woman? If she covers her face to hide the delicate features, baggy clothes to hide the buldge of her breasts, black wardrbe to hide her curves, or a scarf to hide her hair, can she really hide what makes her a woman? Doesn't the black really define who these women are and make them recognizable as women?
There has been a fundamentalist movement in this region to force women into covering more and more based on the above-mentioned argument that the current clothes do not hide enough. And the more these women cover, the more they are asked to cover more, and the more they are harrassed on the streets and seen as walking vaginas.
These women, no matter how they act, what the accomplish, how they carry themselves, and no matter what they wear, are always seen as sexual objects; they are trapped in a prison that is their vaginas. They can become government officials, soldiers, intellectuals, artists, or anything else, but they are not seen as who they are or what they do, and they are stll defined as a hole made for the pleasure of men and for bearing children.
If these women cannot satisfy their societies with being respectful members of the community, covering up, and also fullfil their duties in the bedroom all at the same time, then what the hell can they do? I have a simple solution.
The only way these women would not be seen as sexual objects in these communities is to figure out a magical/scientific way to remove their vaginas and leave them at home for the time they are to be used. Maybe even for those who do not wish to use them, get a "vaginectomy" and get rid of it once and for all.
Let's assume this is possible. Do you really think these women will stop being treated like peices of meat, like sexual objects that exist for sin, or will allow them to be fully functional and respected members of society?
The reality is, the vagina is not the prison for these women; their backward, sexist, authoritarian and patriarchal societies are. Hiding who they are and what makes them women will not free them, but will add shackles to those already pulling them to the ground.