you're drawing a strange parallel to "giving up", its not giving up in the sense that you have some thing you need to accomplish and you're choosing to quit, hair loss isn't a binary thing that is easily achieved.
I had a friend who was holding on to like a few strands of hair on his head, was very late to the party to intervening with medication and was also an incredibly paranoid person so he would never consider it anyway, he didn't have enough money for surgery, and for him his best option was truly shaving down and letting go of the little bit he was keeping that looked a lot worse.