It's a little of both tbh. Why would it be a bad suggestion ?
Edit: Mother of god, I've created a monster! All I wanted was to make a reply, but then I just kept writing! Someone stop me D:
I don't want to decrease hp or buff overall damage. I kinda like that it's not always about who gets the first hit in. This is how it ought to be for anyone wearing armour, even more so for plate. This means that getting a lucky hit in, while giving an advantage, doesn't end the fight (except for those damn super STR guys). Having a decent time on a melee fight unless you are completely rofl-stomping someone is a good thing. What I would prefer is having it so you (against armoured enemies) need to get multiple hits in before they die. This takes skill because you not only have to get past the defense of an enemy, but you will have to do so repeatedly while still maintaining your own defenses.
Personally I would like to increase the importance of armour (especially against cut) while keeping it so any "correct" hit would still least cause a stagger (maybe even 0 damage attacks should stagger if it is timed right) and reduce the effectiveness of STR.
Give the anti-armour weapons a nerf, but make it so that they are almost required to use against someone in full plate. Give some incentive to go into battle with more than 1 weapon. I'm all for all classes having a fighting chance against every other, but also giving that for weapons and armour is a bit over the top. Sorry to go realism, but most people didn't go to battle with 1 weapon. They carried knives, daggers, hatchets, additional sidearms like maces etc. Let us get some reason to bring them out. This could also mean making halfswording more decent. See plate? Sorry, but you will have to halfsword his ass to get through, or stunlock him with your non-penetrating cut swings until an ally stabs him with an awlpike or bashes him with a maul.
As I mentioned, it would be nice for attacks that do 0 damage due to low PS or cut vs high armour (but not because of hiltslashing/hitting early in the animation/bad angle) to still stagger an enemy. Sure, even if you don't penetrate their armour to damage them with your cut weapon, you still hit them hard enough to interrupt their swing against you, giving you time to switch to a secondary weapon or halfsword or flip your weapon around (from cut to blunt, like the axes have).
Right now STR is Survival (IF) AND damage (PS/PD/PT), while athletics is only mobility (athl/riding) and accuracy/hybriding (wpf. only 100 needed for melee). Most people don't use ranged or multiple weapons (why is this? I would love if going into battle with only 1 weapon was a BAD thing), so if you have to choose between Damage AND Survival or Mobility, why go for the 1 out of 3 instead of the 2 out of 3?
Ofc, as it is now, ranged needs to same amount of hits to kill someone (not counting high STR in both the hitting and surviving part), so that needs to be changed. I always wanted to look on ranged as something that kills only unarmoured, wounds armoured as they move closer and then pick up a melee weapon when the enemy gets close. That's how I like to play as an archer and I still do. A mace, pick or hammer and 6 ps is good enough when your enemy is at half health (or less) after you shot them.