I didn't really watch Two and a Half men but as someone who is an apologist for Married with Children and Al Bundy....the thing about that character is that the show not only frames him as being flawed, misogynistic, and terrible: it actively and very sadistically *punishes * him for it. In fact the tragedy of Al Bundy is that he and his toxicity are almost always the instigators of his suffering on the show...which is why you sometimes can't help but find yourself rooting for him. Hoping maybe he'll grow as a person.

...I don't get the impression that's how Charlie's characterization is approached.