Irelia is not the problem, Conqueror is
Let's take a moment of pause and think for a second (ok, I know I'm asking too much of some players, but hey, do it for me).
Before Conqueror was released, Irelia's kit was considered weak after all the nerfs she got post her release when she was indeed too overtuned, then suddenly a new rune pops up, and she's Top Gun.
We all know that Conqueror in it's current form isn't a healthy rune, yes it gives something to bruisers to fight against tanks, which otherwise would just demolish them, but the rune itself is too overtuned.
If Riot would nerf or rework Conqueror, Irelia wouldn't be such a problem, she wasn't prior to the rune, so it should be obvious that the rune itself is an issue. It gives her too much dueling power early by giving her a lot of AD and the True Damage.