What to do when reviewer wants p-values, but I prefer to use significance stars to prevent clutter in table?
In general you are not obliged to comply with all reviewer wishes in your revision, unless maybe the editor has mentioned such a point explicitly in the decision letter. If you don't want to follow a reviewer's suggestion for revision, just explain in your response letter in a factual way why you choose to do so, and see what the editor and reviewer think about it. You have good points for such a response in your question already.

I would nevertheless suggest to make the reviewer's life as easy as possible. Even if you don't want to have them in the paper, you could maybe add a list of p-values to the response letter for exactly that comment, stating that for the convenience of the reviewer you calculated the p-values from the data given in the paper (instead of expecting the reviewer to do this). You could also offer to put such a list in any supplementary material if the journal has such and the reviewer thinks it's important that readers see that.