The thing is, it's not true that all of them would die. All of them would die except for one. And the winner would have a life of glory and luxury instead of drudge and misery.
In the "real world," why do so many poor youths focus energy on dreams of being a sports hero instead of the more tedious but realistic preparation for good grades and everyday life skills that could better serve almost all of them? The chances of being the next Michael Jordan, Tom Brady or Christian Ronaldo are millions and millions to one.
Why do people with limited means spend five, ten bucks or more on lottery tickets several times a week, almost certainly flushing that money down the drain, when there are so many needs for those funds in other aspects of their lives?
Why do people go on to be contestants on the "Are You Smarter than a 5th Grader?" TV show? By definition, they're going to pick people who are probably questionable in regards to being as smart as an elementary school child. However, contestants are sure that they must be smarter, not considering that they probably never would never have been chosen if it was that obvious.
The dream of "hitting it big" defies practicality. The idea that "someone is going to hit it big, and I have as much chance as anyone else" overrides the reality that the "as much" chance is close to nil, and, that while someone will hit it big, that number is almost impossible to see when the pile of those who don't is put next to it.
Everyone is taught that anyone can achieve their dreams. While the reality is that real life is much more likely to chew you up and spit you out, that reality will manifest itself soon enough without adults crushing the souls of kids and youths from an early age. So we allow them those dreams, because, maybe, it will be our special child that wins in life (even when our souls are crushed by life, we retain that fantasy for our kids), but only if they aspire and try.
Circling back to the world of the Hunger Games, for many, the spectacle and treatment they get merely by being contestants is beyond anything they ever could have imagined in their home districts. Even if they consciously know and mentally acknowledge they are probably going to die, obsessing and being miserable about it isn't going to change that. Being a fabulous super-celebrity, with all the perks, is something that is hard not to get caught up in, even if it's for something that will be eventually tragic.
EDIT: Plus there is the very clear implication than runs through the fanfare that, if you don't play along, and instead anger the organizers, they can make very sure that what slim chances you may have had, going in, will be taken away.