Jax builds AD anyway though - at least at the high level play. It's exceptionally rare to see Jax with a Hextech or Guinsoo. Same with Poppy, Akali, Kayle, Katarina, and Eve, they all build almost exclusively AP or AD even though they have scalings for both, so the 'hybrid' is just built into the character. The mixed damage works well against squishies, who can usually only get 1 defensive item, but it is worse against fatties than dedicated AP or AD damage.
Obviously this is just all leaguecrafting though, you run into all kinds of situations in games where anything is possible. I have no doubt there's people with wins as AP Riven out there. I'm mostly just talking about the theoretical optimal builds, which rarely come to fruition anyway.
For what it's worth, AP Jax is my favorite non-traditional build that I started doing because of theorycrafting. It's fun as hell but viable in like 1/2 the games of a regular Jax build.