Why? Because there is no real prize--just a trophy and $25,000. That's barely a pittance in tv money. The real prize--and I'm sure the reason that so many contestants are willing to compete--is performing their act in front of millions of viewers (and booking agents for Vegas and other venues) for several weeks. Such exposure is extraordinarily valuable.
Listen to the backstories of many of these acts. Even the "losers" are not really losers. All of the good acts have been busy performing all over the place. Many even have their own show in Vegas. After all, on any given night, Vegas has hundreds of performers in the casinos and clubs. And every time that some fourth-place finisher signs a contract to perform in Des Moines or Omaha or Tallahassee, their fee gets bumped up as the promoter can bill them as "AGT finalist!"
The prize is