Taking your argument further....
If we take your argument and apply it to another of the proposed problems, the existence of Cowell, I think most would agree he exists because a large group of today's youth are driven by the media to aspire simply to "becoming famous". Therefore, following the Free School Meal solution, we must either meet the incentive or remove the incentive. Making everyone famous is not realistic so we need to remove the desire to become famous. I can see two ways of doing this.
1) Careful regulation of all media to show how becoming famous is not the be all and end all of existence and that the famous are generally no more happy than the rest of us. This all seems a bit far fetched and I don't really see it working in practice
2) A hunger games style elimination of 100 "celebrities" each week or so. That should cut down on the number of people wishing to become a celebrity, provide TV far more watchable than X-Factor or BGT and, as an added bonus, should I be allowed to create the list of "celebrities" I have a sneaking suspicion Cowell will cease to be a problem.
Ahh, economics at work!