I don't see any reason to reject the possibility out of hand as a matter of design.
Oh I completely agree; to be clear my whole point is that
neither system should be rejected out of hand; as I said it's only personal preference that leads me towards the per-item system. It has advantages (it's much easier to balance because of the smaller range of possible damage reduction factors, avoidance of risk-free combat and silly wardrobe choices, etc.) and disadvantages (greater complexity, built-in randomness, etc.) and you can only really judge the overall merit of any armour system within the context of a game design as a whole.
One thing to remember is that increases in randomness *always* are to the disadvantage of the player character.
I broadly agree with this (indeed, the game I'm currently making has completely deterministic combat) but with the caveat that I don't think 'always to the disadvantage of the player character' necessarily equates to being always of disadvantage to the player's
enjoyment. I think that randomness has its place in the game designer's toolkit, even though it is often used badly. For instance:
Armor protection is the same way. The more randomness it leaves in the damage the player is taking, the less it matters to how the player will have to play and the player's odds of winning.
There's a flip-side to this, which is that if combat is very deterministic and you have high enough armour and/or HP that the enemy you're fighting can only do inconsequential damage to you each turn, the action you take next turn also doesn't matter that much because a 'bad' decision won't have any serious consequences. Ideally, you want to avoid either extreme in order to keep the player's decisions meaningful.
Which is a major reason why I slightly shy away from cumulative damage reduction; the more armour you can stack up the less significant the consequences of being hit until, on a turn-by-turn basis, you don't really care that much whether you're getting hit or not. To combat this the designer might introduce more powerful enemies which could easily one-shot a character without heavy armour, making unarmoured playstyles much less viable and the decision of what kind of armour to wear less interesting. With a per-item system a full suit of plate-mail doesn't give you a maximum damage reduction any greater than just having the cuirass; adding extra pieces to the set just increases the odds of you getting that maximum damage reduction, so it's a question of managing vulnerabilities rather than just gaining a flat rate of damage reduction. Your damage reduction range can be much less and so your potential damage range can also be less. Of course, it's all a matter of balance and with care either system can be made to work successfully.