Damage thresholds can lead to funny unrealistic realisms same as AC (ie % reduction of any hit independent of power of said hit looks weird).
That's why you should have a flat amount of damage reduction not %. Helmet that decreases all damage received by 5 doesn't cause mentioned problems.
And instead causes more serious problems of requiring characters eat tons of hits like nothing. It's also really whacky to balance since early armor can't have significant DR which makes it worthless. It only kinda works in games with non-human units where armor is a weight consideration (light, medium, heavy) rather than something that progresses as the game goes on.
I don’t see the issue. Light armours restrict movement and agility less, ie bowmen and scouts who can travel or retreat faster and further with less fatigue. Heavier armours are costly and not something adventurers would start with unless coming from wealth or nobility. Then there’s magical enhancements to armours which give you progression. The whole point of armour is to mitigate hits.
aka the D&D AC system is antiquated and painfully unrealistic when used in computer games. A full plate tower shield fighter uses the same armour system as a 30 dex elf in red undies. One would realistically be harder to corner and hit and the other would be much harder to physically damage yet with the AC system they are calculated the same.
Think about it for a few seconds. How much damage does a single hit do, how much HP does a character have, and how much reduction is needed to make the armor's damage reduction meaningful? Can't be too low or the armor does nothing, can't be too high or armor is everything. Then try working out how you increase the armor's effectivness without breaking that careful balance.
Look at the extreme examples. If an attack does 110 and character typically have 100 HP, that means armor needs to reduce damage by 10% to be worthwhile (turn death into survival), but then any armor value between 10% and ~55% (where it lets you survive 2 hits) is largely wasted (it makes healing easier, but otherwise won't let you live long). On the other hand if an attack does 25 damage and characters have 100 HP, 1% lets a character survive another hit, but the next won't come till over 35% reduction, and the next won't come till even further, and is turning 4 hits till death into 5 hits significant in the first place? Armor as damage reduction requires damage sponges to "work" mathwise.
The problem is you are taking a more realistic armor system, yet keep applying it to the same old HP system.
Change how health works, and the armor system becomes a lot more useful.
Let's take a blood loss system instead, for example. A successful hit will cause a bleeding wound. The depth of the wound determines how much blood is lost per turn. To stop the blood loss you need to apply a bandage or seal the wound with healing magic, which is not always possible in the middle of a fight. Armor that can entirely block a strike or brake its force so it inflicts only a lighter wound would be of extremely high value in such a system. Add other wound effects that can reduce your combat effectiveness, such as a wound in the arm reducing the force behind your strikes, and armor becomes even more valuable. Then make the armor system locational and you have a trade off between full protection and mobility. Do you only wear a breastplate and helmet because those areas of your body are the largest and easiest to hit, and can suffer the worst wounds, while keeping your limbs free? Do you try to penetrate an enemy's breastplate to go for the heart, or will you try to wear him down by hits to the unprotected arms and legs? Having a dozen shallow wounds on your arms will still wear you down from blood loss, but maybe you can outlast your fully armored opponent in the fatigue department because he carries more weight and therefore exhausts more quickly.
Don't just slap a complex armor system on existing HP systems that are all about reducing a big number from 100 to 0. Re-think how health and stamina work.