That heavily depends who and when you are fighting.
Yes. If you are only ever going to fight other rich people on a formal battlefield and the other 95% of troops on the army aren't going to come within a stone's throw of you that's fine. However, thought it may sound cynical the primary killing duties of the rich noble on the battlefield involved killing the opposing peasantry.
Field plate wasn't that uncommon after a certain point in time.
"Reduced plate" armor really only became more widely produced in the 16th century. At that point the advanced crossbows, black-powder firearms, and cannons were on the scene and started making the point moot. We're at the beginning of the end of personal armor, first bulking up to stop the arquebus and then falling away as the superior penetration of the musket and improved cannon accuracy. It would segwayd directly into the 17th century model of the smallsword, pistol, musket, bayonet, and petard.
I generally peg my D&D into pre-black-powder periods, but that's just my tastes.
And most other things are not modeled in D&D.
Yes. Discarding / breaking your weapons isn't fun so the game hand-waves stuff like that. Swords cut chain, spears and lances don't break, and axes don't get stuck in anything that isn't a Baaz Draconian. If D&D weapon performance vs. armor is accepted as natural in the game world then the superior penetrating power of the ax and hammer are moot anyway. The sword is basically -never- the wrong weapon for the job like it would be on the real-world battlefield.
Sword, ax, or hammer - whether you want to wield or enchant one or the other would be purely a cultural or aesthetic decision.
- Marty Lund