Being stripped of a star sends a very strong signal that the restaurant/chef is in decline. It will certainly be harmful for their reputation and business.
thats not the point. for a three stars loosing a star is loosing money which means loosing quality, you can't afford to pay top notch cooks, they leave, you loose more quality, you have to lower your price, you buy cheaper products, you loose quality...
But instead, he wants to lose all three stars? There's undeniably something irrational about his request.
If he's willing to lose stars to get rid of the pressure, he can simply ignore the judges.