I think the reason why there is no br in halo 3 odst is because the odst team that you are with(as the rookie) didn't think they needed them heres one possible reason why. They, meaning the odst team you are with, thought that the covenent were staying on earth, no one expected regret to go into slipspace. The UNSC and ONI knew that a covanent leader was on the crusier and they planned to use the Master Chief and these odst's to infiltrate and rendezvous inside the carrier and capture regret. They Expected it to be close quarters thats why the had mostly short or long range weapons they didn't need the br or they probably thought, onced they rendezvoued with chief, they would be resupplied (they were entering at different parts of the ship). Then regret went into slipspace and the odst's where left on earth while In Amber Clad took the chief and possibly most or mabye all of the br's. That is just my theory if you have any questions or theories of your own please do not hesitate to ask or write your theory.