I suppose if he's summited the other six highest points already, then it may be within hailing distance of sensible to let him attempt Everest. He would already have risked his life many times over to get to that point, and would at least have some high-peak skills and experience. Denali and Aconcagua are no cakewalks. The antarctic high point, either.
As for him succeeding and holding this "record", I agree that it is a perfectly senseless record to hold, and it bestows the kind of pointless fame that won't do him or anyone else a bit of good. AS for it being his "dream", not every dream a 13 year old conceives is worth encouraging.
I just hope he comes down alive, with all his fingers and toes intact.