The advantage hard metal weapons have over softer ones are that you can put more force into the blow.

So while this is definitely a "game" mechanic. You can think of it as better weapons allowing you to spend more effort while keeping within the limits of given weapon.

We can think of harder weapons as being sharper therefore having more damage, but IRL it does not really work that way. Swords arent actually that sharp, its all about ergonomics and how much force you can put on the target. Stiffer metals offer significant advantage here.

The advent of heavy weapons and armor had just as much to do with metals as wealth of army employers being big enough to support dedicated soldier jobs that could reach and remain fit enough to employ them, as well as all the logistical requirement around it.