All true, just want to add to it.

You can bring the mace anyway, just in case, as long as you don’t mind carrying it. One other major benefit is that the things could be dirt cheap because you don’t need good quality metal.

But if you want to hit people, and have a money and time for training, go for an axe. Pretty much all the advantages of a mace, but can cut on top (and usually poke too).

The other part of the equation is not getting killed, and usually the guys in heavy armor are good at killing you. Getting in striking range for a medium range weapon like a mace/axe/sword is damn dangerous, so a slower weapon like a mace or axe that’s additionally bad at defending because of a more distant point of balance means a much increased risk to your life. So if it’s one on one, you should really think twice about trying to getting that lucky strike in.