The reason Jax is not viewed as a problem compared to things like Irelia and Aatrox is that he has much, much lower pressure in lane than either of those champs. Except for a couple key matchups like Yorick and Trynd, he doesnt' really bully anyone in lane. And then when you look at his impact on the rest of the map, he just takes longer to come online than things like Irelia or Aatrox. Both of them can CC from much farther away and have ways to get out. While in the earlier stages of the game Jax leap is usually a one way ticket in, and then he has to be in melee range to stun. It's just way more risky for him to go in, and when he does go in, his burst damage is weaker than both of those other champs until much later in the game.
Here's what I will give you, when Jax does get a lead and start snowballing, it's a freaking avalanche. But again, outside of a couple key matchups, no one should really be getting knocked around by Jax during lane phase. And pretty much all of the other fighters and tanks have more agency than he does early on. As far as counterplay goes, I feel like it only seems that way when you're playing another melee AD champ or Tank. He can definitely be hard kited by team fight comps, I just recently played a Jax game into a Janna, Orianna, Caitlyn with tank top comp, and it was a freaking nightmare despite having smashed my lane. Same deal with poke, as his E dodges autos only and his ult is pretty short duration and therefore reserved for the all in. I mean Jax's ult scales with AD/AP, and currently he builds heavily into AD, so mages with high sustained damage like Vlad, Swain, Cass are always very strong into him.
So when you say "no counterplay" I'm assuming what you mean is that in a context of a 1v1 he pretty much outscales everything in the game. But that automatically points out a weakness in a champ as getting a sustained split pushing going is harder now than it used to be, especially in solo Q. I actually think Jax is a really good example of what scaling looks like. In my opinion, all champs should scale proportionally. By that I mean lets say every champ has 10 power points, and during their design these 10 power points are to be distributed between the early, mid, and late game. Jax works because his early game is not very good, and his mid game is pretty bad, so his late game gets to be literally best in class. It's a fair trade off. Compare that to Irelia, who seems pretty equal to Jax very early on, but hits her "mid game" spike a bit earlier and then is just nuts from then on out. It just is not proportional at all. Where Jax power points are like 2-1-7 in terms of early-mid-late power, Irelia is like 2-6-5, making her overall just way more valuable and less risky. I'd say Yasuo has the same issue, where his supposed mid game power dip is not nearly big enough of a trough to justify how easily he can push people in early on without taking too much harass and how well he scales.