I don't recommend you watch their D&D stuff then it might upset you. Interestingly I find your example a great illustration of why sticking to the rules limits play. If course a glaive and halberd are different, and the fighter could use the axe head to fell a tree (though they probably wouldn't want to) or get the head stuck in a fallen enemy.
Character sheets being available would just make it more obvious where they are making things up.