Looking at this from the individual level, competition teams for BJJ are a brilliant idea as far as I can see. The process of being selected, and then preparing for the tournament involves a fair deal of training; this extra pressure and level of intensity is great for an individual's training.
Looking at the bigger picture, having teams compete do help raise the profile of the art; something which can only help BJJ schools grow, and improve the quality of events as time carries on.
I'm going to be in a team competition on May 8th down in Birmingham, and I'm quite looking forward to it - I have a positive opinion of team competitions at this point, and I believe they can only help the art & the competitor.
As for the issue of teammates not fighting each other, I think it is disrespectful to not fight your teammate if the situation arises - I have fought people I consider friends and teammates before at competitions, and neither of us have had any problem with it.
I have seen guys play rock-paper-scissors at a competition (I kid you not) to decide who wins the fight, and personally do not agree with it.
Most team trophies are really just who had more people show up to the event, nothing to do with skill. Its a way for the promoter to offer something to the large school, recognize them and make them feel special so they sogn up lots of competitors again for their tourneys.
I true team award would be done alla high School dual meets in wreslting. 8 on 8 or 5 on 5 whatever representing the best of each school with one man per weight class as a team on team division.