The mystery of the electron's spin

From "Is space like a chessboard?":

The standard cartoon of an electron shows a spinning sphere with positive or negative angular momentum ... However, such cartoons are fundamentally misleading: compelling experimental evidence indicates that electrons are ideal point particles, with no finite radius or internal structure that could possibly “spin”.

Thank you. I have long puzzled over that "standard cartoon" in popular accounts. I was aware of the obvious problem with this picture yet it has been invariably presented as though it were a perfectly clear and correct account of electron spin. This confirms that the expert physicists offering this model didn't really understand what was going on either. They were just faking it.

PS: They may have developed a new clue, but I think they are still groping for a real explanation.