I think the main problem with Jax is not himself but his counters. I mean, Jax is not undefeatable, even in 1v1, neither at early, mid or late game, but the problem is that they get destroyed by him outside a specific time range. Lane counters are pretty much good against him at early, but at some point Jax will be able to win trades and keep farming even with a kill disadvantage if the game goes longer, and may bring more to the team than the other solo top.
At the same time, at late game, he has no chance 1v1 against an enough farmed Sion or Nasus, but these will loose the lane early game against him.