Informed trader needs to be properly defined. Suppose a person just does some research at individual level (read, OSINT, make their own computer models to do prediction etc), then that's permissible.

But if you're defining an informed trader to already know the answer, then it's problematic. I hope you see that as well. The market should reward some logically deduced conclusion, not power. That's my position.

Also it's not noise, an average trader is not choosing a random number between (0,1). They can do research and their guess can be informed. Hence, the use of word wisdom. By your definition, this is gambling then.