|Armor and Magic Resist are interesting choices - which you need, and when, is a question of who the big threats on the other team is. Your order for them will vary game to game and some games - if no dpser is doing particularly well, or you're getting super fed - you might not need much of them at all. But Health? Health is always a right answer, unless you artificially insert a reason why it isn't a right answer, because the other team WILL be doing damage and Health counters all damage equally.|
Secondly, the power of Armor and Magic Resistance is a multiplicative statistic to your own defenses and a penalizing statistic to the opponent's lifesteal and vamp options - this makes it so that things like Shields and the like are the primary power source.
Finally, Armor and Magic Resistances are *still* go to defensive statistics - you can never make them irrelevant because they are multiplicative scalars. People aren't stacking raw Health in the competitive scene - It's true that their builds are dominated by items with Health on them - but it's frequently a heavy mix of Health and Armor (Omen/Locket/Bulwark) for example.
Even if all of that weren't true - it's still important that options have weaknesses that can be directly attacked - because otherwise, you tend to get into a steady state where certain things are "accepted" to be norms and then everything else in the game has to be balanced around that. For example, the prevalence of armor and the strength of the AD carry physical damage options meant that for any character to deal relevant damage late game that wasn't a carry - had to have either enormous free resistances or enormous piercing to even be relevant.
If you make Health really good earlygame, you will have to bandage that by releasing a 'counter' to it mid-game, eh? Now everyone has to build those two items, every game.
That is a myopic design path at best: You cannot be making single-structure counters to baseline systems.
You need to foster emergent and diverse gameplay by offering items not which counter a particular build, but which aid a champion to perform a design goal you have set.
Do you want Ranged AD to counter tanks? When do you want that to happen? Do you want tanks to build Health? Why do you want these things?
1. Ensure that counters exist.
2. Ensure that the counters aren't too hard and that other strategies can be competitive even if not directly countered.
I've stated this point several times - in fact several times in this thread that #1 needs to exist to ensure that item builds don't gravitate towards the things with least counters.
And that #2 needs to exist so that competitive strategies can arise to deal with things indirectly.
What happens if that counters don't exist in a cycle is that basic human risk aversion will tend to gravitate builds towards whatever the safest option is, rather than the one that makes the most sense for the character that they are on - and what results for that in that the options for attacking those characters become the same, rather than whatever makes sense for the character that you're on.
It's important to realize that every champion starts somewhere differently on the Armor / Health / Damage / Shred axis. Renekton and Cho'gath for example, sit high on the health axis, innately, due to character kit. Rammus and Leona, for example, sit on on the resistance axis. Tristanna sits high on the Damage axis - while characters like Jarvan already sit on the shred axis - hence why item cycles exist in the first place - because character cycles already exist - and you want to avoid things being solely determined at champion select. In a universe where items are being built to simply augment innate strengths - you tend to fall into a case where champion selection is frequently the only thing that matters and frequently one that cannot be played around meaningfully after the game starts.