Kryptonite might have been useful once upon a time when they needed some plot device to weaken a guy who was so powerful that he couldn't get hurt by anything else and was top of the totem pole.
But in the last few decades before the reboot it became variously a writer's crutch, a cliche, or a joke. Nearly every movie he got taken down with kryptonite somehow. Whenever he was with Batman or whoever on a mission, the villain would have kryptonite so Batman/partner could do something. Nearly every damn episode of Smallville, Clark got taken down by the stuff, sometimes just by randomly running into it. It got to the point where every time Clark went to confront some antagonist, you just waited for the green stuff to come out (on purpose or by accident) and Clark to hit the floor. You'd think he would have developed some sort of psychological problems and been afraid to leave his farm there was so much of it around.
Supes later on wasn't nearly as powerful or invulnerable. He wasn't so much more powerful than other heroes/villains that he couldn't be threatened or beaten by them. He accumulated other weaknesses like magic and red sun radiation and power draining that were nearly as bad as k-nite, to the point where even a planet of Kryptonians could be quickly beaten by earth in a war and plenty of heroes could take them down.
In short, why do they still need a kryptonite/special weakness? They don't need it anymore. If they have to have it make it exceedingly rare (won't work because writers are lazy), make it just an annoyance, or make it deadly to ordinary humans.