The last people I would trust to run the world are celebrities, but one must consider the method of election of representatives, senators and the president. It is nothing more than a popularity contest, one could argue quite reasonably that we already have allowed celebrities to run the world.
In the senate, and the presidency, such a thing may not be that bad, but it is the flaw of the House of Representatives, which if we had remained true to the founder's intentions would be a much bigger body (1,700/10000+ depending on methodology.)
Instead of one representative "representing" 700,000 people the first would give one representative per 200,000 and the second would give one per 30,000, thus ensuring that more people would have a vote, and it would serve as a way to allow more political parties to get elected, thus ending the duopolism of the Republicans and Democrats.
No, the real question is, do we want to continue allowing "celebrities" to run the world?