All created quizzes on the site have to be attached to someone's name and profile and, in the case of team quizzes, that name has to be the person who created the template. You would receive the reward for it (if any) but at the same time it would always be attributed to your team as a whole. If you check on the team quizzes on the homepage (eg. http://www.funtrivia.com/trivia-quiz/General/Why-2k--360042.html
) you'll see that it links directly to your team.
Benefits otherwise? Your team gets good practice. Writing one question in a team quiz and collaborating on the effort (from initial writing to editing and, possibly, corrections) can be easier and less stressful than writing a full quiz, right off the bat, on your own. I consider team quizzes to be both a great exercise for the team and a great 'gateway quiz'.
The five-quizzes rule is put in place so that the rest of the team does have someone to fall back on. At that point we have a feeling for an author's capabilities in the queue and that person can very likely be trusted to open the template, edit the submission, and keep the questions/people in check so that we receive a sound quiz in the queue. While others in the team can always take on the editing role as well, it's a way for us (the editors) to have someone to refer to for notes and the like. The person who's attached to the quiz receives the corrections, for instance.