Why to build armor/magic pene , when health protects you from all kinds of damage?
First - because 2 x 2 x 2 is better than 2 + 2 + 2.
LoL is a game where stacking a large assortment of stats rather than focusing on 1 stat is optimal.
HP is effectively multiplied by armor vs. physical damage and magic resistance vs. magical damage. At a certain point, armor and MR are just going to be more cost-effective than HP.
If you have 500 HP, a 500 HP increase is pretty massive - you're doubling your effective health, a 100% increase.
Alternatively, a 50 armor increase is only a ~50% increase in your effective hit points (EHP).
If you have 3000 HP, a 500 HP increase is a measly ~17% increase in your EHP. However, that 50 armor is a ~50% increase.
LoL isn't a game about finding 1 good stat and sticking to it: it's about finding a good stat and getting a higher ratio of that stat compared to the other stats available, but still getting the other stats available.
As a tank you want armor and MR.
So you get armor and MR on them.
Second reason:
flat penetrations are...special.
20 armor penetration vs. a target with exactly 20 armor is going to make you do TRUE DAMAGE! A solid 20% DPS increase at that.
20 armor penetration vs. a target with 200 armor...is not. That's a hair above a ~7% DPS increase.
Vs. early-power items like
, you can, quite awkwardly and contrary to what the name "armor penetration" and "magic penetration" implies, counter armor penetration or magic penetration harder than they counter your armor or MR.
Some high-end items like
even predominantly feature flat-penetrations as a major selling point. A handful of champions also have flat penetration skills, so it's a useful trick to know that armor/mr are actually really effective at shutting that down.
It's not like AD or AP see a diminished DPS increase vs. higher health.
Third reason:
everything that's tagged as a "healing effect".
HP/5, jungle camp healing buffs, life steal, spell vamp, self-heals, healing abilities, healing potions, health relics...
If you have 2000 HP and restore 100 HP, you only restore 5% of your maxmium health.
If you have 1000 HP with 50% damage reduction and restore 100 HP - you restore 10% of your maximum health.
Same effective health in both cases - but the same flat value heal is twice as good and scales even stronger with %damage reductions, where a flat HP increase doesn't improve what healing does at all.
The same can be said vs. hostile life steal/spell vamp.
If you have 2000 HP and an opponent hits you with a 100 damage attack with 20% life steal - they restore 20 HP.
If you have 1000 HP and 50% damage reduction, they only do 50 damage and only restore 10 HP.
You don't have to be Mundo to appreciate bonus healing, healing is so important for the first jungle clear armor is preferable to health. A large number of tanks and fighters also have some pretty impressive sustain in their kits.
Also taking a dump on
has it's uses.
When you have 100 armor, how much damage do you take from a 100 ad dmg?
Easiest way to remember how armor and magic resistance scale is this:
100 armor is 1/2 damage taken
200 armor is 1/3 damage taken
300 armor is 1/4 damage taken
400 armor is 1/5 damage taken
500 armor is 1/6 damage taken