It's due to the nature of AP and AD.
AP is mostly burst, so building MR feels more impactful because you see large numbers resisted all at once. However, building MR won't feel as good when fighting someone like Amumu or Rumble since their kits are more about drawn out magic damage.
AD tends to be lest burst and more drawn out. Where someone like Viktor or Veigar can dump their whole AP kit on you at once, ADs tend to take longer. That's why armor seems to be less effective because you tend not to see these massive numbers reduced since they're smaller and less significant.
No, you cannot build a zhonyas and expect to be face tanking AD. It's got an extremely powerful active for many scenarios. And armor items tend to have higher armor values than MR items due to the flow of AD damage to AP.
Zhonyas is not useless, it's finally just not an overloaded AP item. A "Good" zed will wait till it's on CD, but at the same time, a good mage will wait until Zed ults. The logic works both ways. League is a game of seconds, and Zed can't always afford to simply wait.
Your post originated on MR vs Armor, but it seems this is just an anti-Irelia thread. Your problem here isn't MR or armor, it's Irelia. She's frustrating and admittedly good right now, but let's try and keep the content and title on the same track here.
In terms of Irelia, yeah. Her synergy with the new Triforce is great. She's a bit overbearing. Triforce works well with her ult, as well as the attack speed and sticking power. Spirit Visage synergizes with her W. It's not as great as you make it sound, but you can't delete someone who build 95 MR, you know? Not counting runes, masteries, and the probability of Merc Treads which is 35 more MR plus any other MR items, she will require kiting.
However, on the flip side, building 95 armor or more will prevent AD champs from bursting you down too. Doesn't mean they can't hurt you obviously, but they won't just steam roll you necessarily. And again, MR seems more potent as most AP damage is burst, so you see larger reductions than the smaller streams of AD that don't have as large reductions per shot. That's the advantage AD has over AP. Constant stream. AP has the advantage of hard burst, allowing the AD to be removed before the stream can finish.
Irelia can do lots of damage, but it's not your whole health bar in one big burst. It's a stream typically over like 5 seconds or so. If it's a 1v1 scenario, well she functions as a duelist so she naturally has an advantage. But in a team fight, your push will fuck Irelia harder than you make it out to.