You are incorrect. Team green does release "day 0" drivers as you put it. Red and Green teams are competitors, and new games are used to benchmark CPUs and GPUs. It's very much in their interest to compete at providing the best performance for the new games. All you have to do is read/watch one GPU review to understand why it is done.
You do not need to update every time a new driver is out, even if the driver is supposedly for a new game you want to play. It's kind of rare that new games will not work with older drivers, but it does happen sometimes, depending on driver version and game developer competence.