at the least it takes away thousands of tokens in the most important part of the context window (!)
also see the comment by comboy on contradictions not helping performance
the system prompt is the most important part of the instruction you can give the model
it comes before everything else + the model is trained to pay extra attention to it
edit: that's also why in smol (minimalist agent harness) there currently is no system prompt at all (you can add one easily if you want to though)
https://github.com/smol-env/smol
the context window is precious
it should be filled with your task and helpful context for that task