On my high school team (349) and with the team I mentor now, we've always had all-student drive teams (with the exception of our 2001 CDI field team which had 1 adult coach). I really think that students can coach just as well if not better than adult team members, and when it comes down to it, FIRST is for the students, so it makes sense for them to be the ones who get to have the great experience of being on the field. Even for people like me who have done FIRST in high school and have experience from previous competitions, I wouldn't feel right knowing I was depriving a student who's actually in high school from having the awesome field experience that I had.
Plus, I think a huge advantage is the interpersonal relationship between students. Students are probably around each other more than they are around the adults, so they know each other better and know how to get across what they're trying to say so that the other person will understand. Plus, some of the best strategy happens when students yell at each other and argue over what should be done and then come up with a compromise (pre-match of course...during the match, not such a good idea...

). Some students might feel intimidated by an adult and might not challenge what the adult thinks is the "right" strategy. In 2001, my high school team voted to select our field teams, and we did the same on my new team this year, and it worked out really well. After building a robot for weeks and weeks, everyone wanted to see the team do its best so they all voted for the best people for the job...not necessarily the people they got along with the best.
Anyway, I guess my bottom line is...often students' desires for the team do well are underestimated, and if you just trust that the students will make responsible decisions about their robot both on and off the field, everything will work out to the team's advantage.