Why would you even say 'please' in a prompt ?
And some people just try to be polite and it only costs a couple tokens.
I suspect it would be just as easy to write a paper that saying please has absolutely no effect on the output. I feel like gpt4 is/was stochastically better on some days and at some hours than others. That might even be wrong though too. The idea that it is provable that "please" has a positive effect on the output is most likely a ridiculous idea.