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.

Something like this should not influence the final decision of the editor. Further, this is not a fight worth having with the editor/reviewer so you should be flexible and accommodating.

You should check past issues and see what the format is. If p-values, regression coefficients, and standard errors are typically provided, you should probably do that. If only 2 are provided, go with those. Assuming regression coefficients and standard errors are typically provided, in your rebuttal letter a statement along the lines of

Following what we think is the standard format for Journal Title, we have only included the regression coefficients and standard errors. As the p-value can be estimated from these values, there is no loss of information. We would be happy to make a change if our understanding of the standard format is incorrect or if an exception should be made in this case. For your convenience we have attached a copy of the tables with the p-values included to this letter.

Subject Matter Answer: You should do as the reviewer asks. Regression stars are vague and non-specific, and amplify differences that are actually trivial. They are a coarser version of the same information, and considerably less useful.

I'm also skeptical that the difference between "*" and "0.46" is what's going to make your table too cluttered.

If anything, the most defensible answer based on "the p-value can be calculated from the coefficient estimates and standard errors" is to drop both.

Academia Answer The answer to what you should do will depend very much on the reviewers, and how big a deal they want to make of this - as well as the journal's stance on it. There are journals I review for where this objection (and indeed, the p-values generally) are likely enough to derail the entire paper. There are others where this is of less concern.

The question then becomes "Is another round of review worth potentially not having to reformat my tables?"

I can't imagine a circumstance where I would answer "Yes" to this, but YMMV.