> Those references are to the recurring gag with Lucy and the football.

Probably, because that's the most popular example of Charlie Brown as a sucker who never learns, but it's a core part of his character and is shown by many, many other gags. There's also a recurring gag with Lucy and April Fool's Day. There's a whole family of them around baseball and Peppermint Patty. There's another recurring gag where he tries to fly a kite.

The comic can't depict Charlie Brown as able to learn - since he never succeeds,† if he could learn, he'd never do anything at all.

† There are a couple of temporary exceptions. When he runs away from home he meets a gang of littler children who respect him. When he has to wear a paper bag over his head at camp, he becomes a success for the duration.