Because most kids can get there parents credit card number, and the "small nominal fee" is often too little and also often too cryptically booked for many parents to realize what is going on or to ask their bank about it.
And because it's just a "small nominal fee" many kids are also not worried about causing any harm when doing so.
Additionally with the credit card e-comerce system becoming more dominant in the world it becomes increasingly more likely for not-quite adults to have something which looks like a credit card for the shop (but likely acts a bit different behind the scene).
Lastly it potentially leaks _a lot_ of private information, which in some contexts is okay but in others is not. Which is also why the small nominal fee trick works, it's often not just based on "only adults have a credit card" but on "let's use the credit card number to get a lot information about the user including if they are adult".