Here's how I would have nerfed jax instead
Counter strike stun duration from 1 second >>>>> .5 seconds +.25 seconds for each enemy champion auto dodged, up to 1 second
This way jax is rewarded for better timed counterstrikes rather than "I'm just gunna activate this so I can jump on you and bash your face in."
Counter strike is hilariously good as a purely offensive initiation tool when it should be more of a defensive tool.
One of Jax's most ridiculous trading patterns in lane is E > Q > AA > W > walk away while you're still stunned. There's little reason to save counter strike as a defensive option when you can use it for a ridiculously strong offensive option. This way if he jumps on you and tries to go HAM without caring about timing E to really dodge autos then you can turn around the fight on him before he can just walk away.
His late game is good but it's not as insane as people make it out to be. He isn't the best dueler and his teamfight is kind of trash. The current nerf is pretty silly and will end up being one of those "well its better than nothing" nerfs.

