Does Allah's command for men to lower their gaze indicate the permissibility of a woman uncovering her face?

The argument that the obligation to lower the gaze from women necessarily implies the permissibility of uncovering the face is weak. This is because lowering the gaze has multiple forms, including looking at disbelieving women, immoral women, looking with lust at a woman's body and face, or at her walk and movement, exceeding what is necessary in looking for medical treatment, looking unintentionally at what is uncovered of a woman, and looking at forbidden images and indecent films, or looking at a woman who has uncovered her face. Therefore, the verse: (Tell the believing men to lower their gaze and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do.) does not necessitate the permissibility of a woman uncovering her face.