Building a 'bot only out of servos would be pretty darn tough.
FIRST/MATE ftw.
EDIT: Okay, more content. What turns me off about those competitions is just the fact that it seems to me that a lot of the bots are more flashy than they are functional; hell, I'd bet a simple robot with all it's allowed weight being put into speed, power, and armor could win without any weaponry at all.
FIRST has lot of aggression with the more recent games, without all the robot-destroying. Unfortunately, it's near-impossible to organize teams efficiently, so each match seems to come down to whether or not each team has a bot to fill each role, or if they can do their jobs really, really well.
Hell, one year we just built a robot that could move and deploy itself as a ramp. Not a lot for us to do for the first few minutes of a match, but we won about three quarters of our matches because we were able to do our ramp thing. (That makes no sense if you don't know the game.)
Now I'm all off-topic. Anyway, robotics competitions are hard to do well. Solo and non-popularized is the way to go.