Suppose you are in a middle of computation on a non accepting state and at this point, an input of 0 is rejected by the DFA. But, according to Sipser's formal definition, you must still draw an exiting arrow for input 0 from this nonaccepting state, which is just redundant. Why not draw no arrows at all for 0?
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.
In addition to what Yuval Filmus wrote, let me remark that the transition "function" not actually being a function but, rather, a partial function may impair the elegance of some proofs (or make them unnecessarily harder). Consider, for instance, the proof of the pumping lemma; in the usual definition, you let $p$ be the number of states and then take a word $w$ which the DFA accepts and is longer than $p$. The argument then is that, when you consider the trace of states which the automaton takes to accept $w$, there is at least one state that comes up twice (by the pidgeonhole principle). This is then used to derive a loop and, hence, pump the "middle" part of $w$.
This argument falls flat on its face when the transition function is partial. Then there is no guarantee the DFA does not stop and accept $w$ previously to running into the loop.
(Of course, here I am talking about the DFA accepting early whereas you were possibly referring to only nonaccepting states having incomplete transitions, but I am sure you get the idea.)