Personal information
COPPA only restricts the collection of personal information. There's a list of what qualifies as "personal information", only one item of which is remotely relevant:
(7) A persistent identifier that can be used to recognize a user over time and across different Web sites or online services. Such persistent identifier includes, but is not limited to, a customer number held in a cookie, an Internet Protocol (IP) address, a processor or device serial number, or unique device identifier;
So if a cookie is set by YouTube and only ever accessed while the user is on YouTube, they're in the clear - it's not being used "across different Web sites or online services".
Biting the hand that feeds IT
