NEWTs and OWLs aren't necessarily requirements to work or survive in the future. Having them just proves you are certified and capable of doing x type of magic at a certain level like any other job in the real world, however experience is always key.
In addition to the Fred and George comment above (leaving and starting up their own joke shop), think of Harry and Ron (who forewent going to Hogwarts for their NEWT year)
"Harry and Ron utterly revolutionized the Auror Department," Rowling
said. "They are now the experts. It doesn't matter how old they are or
what else they've done." - Interview with JK
The Triwizard tournament is also a HUGE deal in the wizarding world. The Champions aren't chosen at random, there is a magic about them being chosen, being worthy enough (not to mention a thousand galleons, that could be invested in the future if they win). The challenges they have to go through are simply extraordinary for wizards, normal older qualified wizards wouldn't stand a chance without preparation. That's got to be worth a NEWT or two...right?
"Why should 'e complain?" burst out Fleur Delacour, stamping her foot.
"E 'as ze chance to compete, 'asn't 'e? We 'ave all been 'oping to be
chosen for weeks and weeks! Ze honor for our schools! A thousand
Galleons in prize money zis is a chance many would die for!" -GoF
Being a Champion also meant that you were gifted in one way or another (or at least seen in that way by other wizards), gifted enough that those credentials that you were a champion would be with you forever and hold some weight in the eyes of other wizards.
Using the most recent Triwizard champions as examples, at least for Cedric, people started treating him like Krum, who was already internationally famous. Note he was already a good student already too.
"Diggory," said Harry. "He must be entering the tournament."
"That idiot, Hogwarts champion?" said Ron as they pushed their way
through the chattering crowd toward the staircase.
"He's not an idiot. You just don't like him because he beat Gryffindor
at Quidditch," said Hermione. "I've heard he's a really good student
and he's a prefect." - GoF
Harry actually saw the same sixthyear girls who had been so keen to get Krum's autograph begging Cedric to sign their school bags one lunchtime. -GoF
Fleur herself was not dim, she was intelligent and gifted, proven by the fact she got a job at Gringotts not 2 years later, backed up by Harry who knew she was intelligent. Gringotts, being the only wizarding bank, would also be extremely hard to get into. Just look at the real world and see how hard it is to work in a bank!
"Fleur's not stupid, she was good enough to enter the Triwizard Tournament," said Harry. - HBP
and Krum was an International Quidditch player, one of the best in the world. His life should be set, especially being just 18 years old.
What about Harry? Well, he's only the main character, the only person to have survived the killing curse...twice, taken down the darkest of all dark lords, and capable of a corporeal patronus at the age of 13.
Also, who would you hire? The 17 year old graduate who has a OUTSTANDING in Defence Against the Dark Arts, or the kid who just took down the don of all evil wizards?
Being seen as a champion put them on a different level to normal wizards. These credentials alone would have been able to get them a job and decent opportunities in their future careers if they didn't have any already.