At level 16 an Alistar using ult typically takes 25% physical/magic/damage. Stacked conqueror effectively raises that up to 31% pre resistance mitigation. That means stacked conqueror enables a champion to do 24% more damage if Alistar had zero armor at level 16. Lets assume for some reason that Alistar decides to get zero extra armor beyond his base from any source. A 1000 damage strike with no true damage is reduced to 250 by the ult without conqueror, after deducting only Alistars base armor at level 16 (94.7), this is further reduced to an end value of **128.40**. Now we add conqueror to the mix: Alistar ends up receiving 230 physical damage and 80 true damage. After resistances this is 118.13 physical damage and 80 true damage for a total of **188.13**.
Congrats! In a worse case scenerio for conqueror where Alistar opts for zero extra damage mitigation that conqueror can aid in penetrating, it still yields an overall damage increase of **46.52%**. Converting only 8% of an AD champions damage gives a boost that massive _at minimum_. This is the most charitable case, any added bit of armor or damage reduction from any source whatsoever makes that guaranteed 80 damage proportionally larger. A rune of all things is the hardest scaling tank/bruiser killer in the game against Braum, Alistar, Garen, Galio, etc, and even allows for a damage output boost of **20.72-41.07%** (Depending on his level and W rank) against a Master Yi that's meditating with no armor bought, and this doesn't even get into the other benefits of the runes.
True damage is not simply "100% armor pen", it goes through EVERYTHING that doesn't outright block damage. Even only converting part of the damage into true damage has a exponential implications against targets using multiple layers of damage mitigation.
While I'm here, lets talk about that healing. 8% of your physical/magic damage regardless of whether it's DoT/AoE and is not reduced by resistances. Lifesteal and spellvamp are post mitigation, conqueror isn't. But also if you hit 3 champions with an AoE it is effectively 24%. This is part of why that fed Riven feels like she's drain tanking 1v5.