I think you’re misunderstanding how the math works. To compute the Mid signal it’s (left+right)/2 and the Side is (left-right)/2. Because of this, all sound that is out of phase disappears when computing the Mid, and conversely, all in-phase sound is removed when computing the side.
I believe an LRmax would probably do what you expect! And I got that implemented today, I’m going to test and make sure it’s useful before shipping it.