I'm under the impression that they don't throw up for a couple reasons. First of all, once the contest is over they're immediately barraged by the media for a while. Logistically I don't think they could find the free time to puke it up for probably at least an hour post event.

Secondly, throwing up that much food strikes me as dangerous. Eating it in the first place is undoubtedly dangerous, but to puke all that up we'd probably be talking at least a solid 50 heaves of maximum expulsion. I can't put my finger on exactly what part of the system I think would break, but at minimum this would have to be a heavily monitored activity to minimize asphyxiation risk.

Third, they train to blunt the vomit response. Eating to capacity and then giving in to vomiting strikes me as incredibly detrimental to long term progress.