I agree with you. We just let our 13 yr old son get one. He's been 13 since mid-summer, but he only set up an account about 2 weeks ago. Why? Only because we are home/virtual/cyber schooling this year, and his cyber school has students across the entire state. The kids have a group page on there (found it thru a parents group set up thru FB) only for kids in the cyber school. They MUST be 13 to join and they cannot use their parents' FB account to access it. It gives him an opportunity to talk with, bounce ideas off of, chat with other kids doing the same thing he is. His brick and mortar friends don't know what "Criterion" is for example (an online writing program that the school uses for the kids to submit essays and things). Or what "custom assessments" are (a bi-weekly quiz of sorts to assess their progress).... But the school itself is very strict about letting the kids exchange any personal information... so they can't exchange email addresses and chat that way. FB turned out to be the perfect solution!
We have his password. And if at any time he does anything inappropriate, we will make him delete/close the account. Frankly, he rarely bothers with it. He has gotten dozens of friend requests from his Brick and mortar friends, from his instructors and fellow students at his karate school, from relatives, etc... but he just isn't that into it. Which is GREAT. BUT, it does serve as a way for him to communicate with like students, if he so chooses.
I think (hope) it will get old quickly altogether. My son has strict rules about what is ok. He is NEVER to type ANyTHING "not nice". If someone is posting "so & so is so gross, they did this..." he is not to comment. Etc.