why not use kryptonite on Zod(follow up of earlier post)

I made a post one time of why in Superman 2 nobody thought to use Krypotine on Zod to fight him, I realized something that a lot of people may not have realized. That maybe the real threat in Superman 2 was not Zod but Lex Luther and let me explain why.
There is a line in the movie where Lex looks down at his ring thinking this would go the distance, which I assume was a kryptonite ring. If there is Kryptonite on Earth Lex either has it or is looking for it. But I am digressing why is Lex the main threat, well in the first Superman lets remember what happened when Superman ran in to kryptonite and its pretty much a cookie cutter pattern of what happens to him every time.
1. Superman or villian flashes Kryptonite on Superman
2. Superman is helpless and weaker than a baby
3. Bystander usually Lois or some person who can not bear to see him this way saves him
4. He saves the day


The only difference between Zod and Superman is if Lex had flashed Kryptonite on him 3 or 4 is never going to happen. Nobody is going to see Zod helpless hurting with Kryptonite and come to his help. Lex can blackmail Zod with the kryptonite, "want me to tell everyone Zod, I can and its bye bye world you rule. I have kryptonite on me at all times you can't touch me" in other words its worse for Zod to run in to kryptoni9te tahn it is for Superman. Is it really Lex who would be running the world?