One thing you're not taking into account is that the ADCs aren't going to stand still, trading blows until one is dead. The C part of ADC is "carry", which means that the team is going to rely on them later in the game to carry the rest of the team.
The ADC, therefore, must make it its goal to deal as much damage as possible in as short a time as possible. If he can't deal as much damage as the opposition's ADC, he's putting his whole team at a disadvantage in team fights.
As a result of this, as you've noticed, the ADC doesn't have much survivability. This is why ADCs are classically known as "selfish" characters. Since they are so important to the team fight dynamic, but also so fragile, they often have to save themselves at the expense of other teammates either by not joining the fight or running early. Positioning is crucial for everyone, but especially so for the ADC; one step out of line could result in a team-fight-altering death.
So while the math may say that overall fighting ability goes up with armor in some cases, that's not actually taking into account the full spectrum of what the ADC needs to do. Hit and run tactics and focusing down targets in the mid-to-late game win out strategically over being able to tank the opposing ADC while you trade blows.
