So why can’t other players detect this behavior and trade with JS, removing their edge?
How would you have identified that there's even such a thing as a manipulation day? Do you have a model that tells you the objectively correct number of days a non-manipulated index should be lower at close?
But maybe Jane Street only traded like this on some days, so you would need to know whether they had done so before you could hope to exploit them.
I know your question was sarcastic, but not everyone is able to see patterns. And not every trader is as good as the other. Hence winners and losers.