I completely understand the guest’s request and never write reviews for a similar reason. I simply don’t like the idea of leaving a digital footprint easily associated with my real identity.
On comments saying people can’t search for your reviews, a program can easily collect any information a random unlogged-in person can manually click and view. I am able to view reviews of previous hosts who have reviewed my potential guests, and with some web sleuthing can also view reviews of those other hosts as hosts as well as guests, and so on. A program can also (slowly) emulate the behavior of a logged-in user.