From a tactical and realistic sense, this is a very stupid and foolhardy thing to do. Almost every time Sups has been in trouble or defeated by a bad guy they were just following his advise and used some form of kryptonite against him.
At least in the first Superman movie (1978) Lex Luther has this to say:
You mean, to us, they're just meteorites. Fair enough. But the level of specific radioactivity is so high, to anyone from the planet Krypton, this substance is lethal!
Now, Lex hides his kryptonite in a lead box. Superman revealed to Lois Lane that he couldn't see through lead, which she subsequently published in her paper. Superman probably wasn't smart to do that.
In the DCAU "A Little Piece of Home"
Superman's attempts to stop the criminals are progressing nicely until he comes near a display of minerals. He sinks to the ground in pain, allowing the criminals to escape.
Luthor discovers the phenomenon and has the display analyzed to discover what happened to Superman. He learns that one of the rocks is from an foreign solar system and realizes that he now has the perfect weapon against Superman.
On the other hand, if you can believe a comic cover, then yes, Superman is an idiot who reveals his weaknesses to his enemies.