I often see students confused/mystified by definitions (and proofs) that allow/consider "useless" cases. A case in point is the definition of a DFA (deterministic finite automaton), which allows states that aren't reachable at all from the starting state; also the proof that any NFA (nondeterministic finite automaton) can be "simulated" by a DFA whose states are subsets of the states of the NFA, again, the vast majority of those states are useless.
When defining DFAs I point out that such superfluous states are OK by the definition, but my students stumble over this anyway. They ask why the definition allows such nonsense. The obvious answer is that not forbidding them makes for a simpler definition, much easier to work with; but it grates their (engineering outlook) sense of parsimony the wrong way.
I'm sure other areas have similar phenomena. What do you do about this?