Why should I add co-authors on Google Scholar?

In general, I find the Google Scholar profile pages to be elegant and useful.

Some people choose not to add co-authors to their profile pages. You might not see any benefit. You might not want to play favourites (i.e., who is enough of a co-author to be listed; what if I forget to add someone, would they be mildly offended).

In general, random people will google you and land on your google scholar profile page. Seeing who your main co-authors are might be useful to such people to give them an understanding of where your work is situated and who you are working with. They can then also more easily explore the academic work of your co-authors.

Because Google wants you to train its algorithms for free (in case they missed one of your coauthors for some reason, or they tripped up on some homonyms, etc). The goal is to have a more accurate graph of research collaborations. In some time, they will probably be able to know for sure who your coauthors are without you telling them anything.

Since they already invented yet another index (the "i10 index"), one can only speculate. Maybe they will publish rankings of researchers. Maybe they will also publish rankings of research groups, defined as groups of coauthors. Perhaps these rankings will be designed to nudge researchers into producing the kind of research that is useful for Google Inc. Who knows. It's a private company aiming for profit; they are not in the business of providing services for free with nothing in return. Your personal data is their product.

(More pragmatically, if you tell them that your coauthor works in a Brazilian university, maybe you will see more ads for plane tickets to Brazil.)