Irelia has Riven Syndrome
For those of you who have been playing for a long time, you may remember this Riven nerf from Preseason 3: > Blade of Exile cooldown increased to 110/80/50 seconds from 75/60/45
The reasoning behind this change was that Riven could simply repeatedly all-in you every time you returned to lane because her ult had very little downtime, and thus you had few meaningful opportunities to take advantage of that ultimate not being up.
Now compare that to Irelia's 70/60/50 ult CD. An increase to around 90/70/50 could be a good start to rebalancing her.