There are two ways to define DFAs. In the more common way, for each state $q$ and symbol $\sigma$ there is exactly one edge exiting $q$ and labeled $\sigma$. In the lest common way, there is at most one such edge.
If you are using the second convention, then you are right that the dead state is not needed. But when using the first convention, dead states are necessary. Indeed, what should the automaton do upon reading $bb$? Any word starting $bb$ should be rejected, but the automaton has to reach some state upon reading $bb$; this is the dead state.