Why can't DFA's have 0 exiting arrows for some input symbols?
This is part of the (usual) definition of DFAs. It's hard to argue with a definition.

While it's hard to argue with a definition, one can ask why the object was defined in a certain way. Here one answer is that we want our automaton to always be at a particular state, whatever happens. In other words, we want the transition function to be a function rather than just a partial function. It is a matter of taste.

Some people allow the transition function to be partial, and still call the resulting model DFA, though this is probably less common than Sipser's definition. The two definitions are almost equivalent – accommodating a partial transition function takes at most one additional "sink" state.