I know how frustrating it can be to be friendzoned when you have your heart set on someone. In this Take, I will explain the silver linings of being the Mayor of Friendville. Since I am a straight male, this is going to focus on males getting friendzoned by females (not friends with benefits situations). Maybe a female GAGer can address females getting friendzoned by males (which is relatively rare).
1. You still get to enjoy her company
There is some overlap between what you do with a platonic female friend and a girlfriend. You can still hang out with her and have a good time. It's also usually much harder to develop a really good friendship with a woman than to get a girlfriend!
2. You are seen with a woman in public
Other women will notice you with your female friend(s) and that will improve your image with them, especially if your female friends are attractive and/or popular women. It will also increase your street cred with other guys- I've had other guys later congratulate me for being with a female friend and they didn't believe me when I said she was just a friend!
3. You don't get too frustrated by rejection
She didn't turn you down because she can't stand to be around you- quite to the contrary. You also learn more about how women think and communicate by being around a few.
4. You get to meet her friends
Assuming you don't already know them, you increase your own friendship circle and, who knows, maybe one of her friends is interested in you.