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What you're seeing is the correct behavior. A single (sheet) body with a divided face. Had the divide face produced two individual sheet bodies, then you would have been able to blank one of them. Compare your result to Split Body, which produces the result you were expecting.
You cannot hide individual faces of a body (sheet or solid). Your file starts with a single sheet body made of a single face, using divide face gives you a single sheet body with 2 faces. If you use split body, you will end up with 2 sheet bodies each with a single face that you can show/hide individually.
Split body can make use of planar curves to divide a body, but you wont get what you want with a closed curve such as you have. One work-around is to use a law extension with your curve and cylinder to create a sheet body that you can then use as input for the split body command.
until recently Split Body was not associative, as you know.
A workaround was to make an associative copy of the body and then trim it from one side to the other.
You can do this with trim sheet.