It isn’t clear why “obscuring the face in public all of the time” matters to anyone, nor is it clear why “obscuring the face in public all of the time” impacts “social cohesion.”
As for this idea that allowing women to choose to wear a veil somehow limits “a woman’s ability to be an individual citizen in public,” the lawsuit clearly gives the lie to this idea. The woman who brought the suit against the ban wants to be allowed to choose for herself whether or not to cover:
The French ban had been challenged by a young Muslim woman who said she sometimes chooses to wear a niqab—a veil that leaves only her eyes visible—or a burqa—a loose garment that covers her entire body with only a mesh over her eyes.
The woman, [a French national who was born in 1990] and identified only as S.A.S. in court documents, said that she wears the veils voluntarily, without any pressure from her husband and family, and that they allow her to manifest her faith. She argued the French ban violates her religious freedom and puts her at risk of discrimination and harassment.
Allowing a woman to practice her religion and make choices for herself doesn’t “facilitate religious rules.” It says, instead, that the state has no interest in whether or not a tiny minority choose to practice their religion in this manner or not. It’s very clear that the woman at the center of this lawsuit can also choose not to cover but feels that doing so is a manifestation of her faith.
Are there some women around the world who don’t have this choice and should they be able to choose for themselves as well? Undoubtedly. Are the bans in France and Belgium designed to help them? They are not.