What's your pet peeve when it comes to tropes? What bothers you when you see it in a show or a movie?
I'll go first. Mine is the instant knockout drug. Like Dexter's intramuscular injection that causes someone to immediately lose consciousness. Or in the movie Split where there's the aerosol spray in your face that makes you instantly unconscious. Or pretty much any time someone uses chloroform.
A lot of that sort of armor is more designed to deflect hits off of it. If someone can get a solid hit in, it's possible to cut through it.
Which leads to another pet peeve of mine, which is armor that's clearly designed in a way that it wouldn't be good at deflecting hits. Particularly anything for women that has cups for the breasts.
An axe could presumably split into chainmail. Although I suppose it's just as likely to just break whatever is behind it. It's not a great armour for large blunt impacts.
Just like there were many forms of armour (plate was very expensive), there were many forms of hand weapons. And although the novels (3ven of the time) tended to romanticise the sword, it was mostly a secondary weapon, much like a handgun nowadays.