It can work, as clearly shown by your rather wholesome example and many people's games. But it's also leaving a very large surface area for problems. Unlike real life, you can just avoid that by making your characters together.

Maybe I should have said in my previous thread that while the "you all meet for the first time" is kind of cliché, there are more serious problems at the game level. And like it can work if everyone makes a fighter, but you can also make everyone's lives easier if you discuss up front.