[cvoss]

The first incompleteness theorem shows that, in a sense, the culprit of a logic's incompleteness is not its "simplicity" but its "complexity": if the logic is rich enough to include Peano arithmetic, then it is incomplete. Compared to mathematics in general, a complete logic system is far less powerful and cannot be used to prove nearly as many interesting things.

[burntrelish1273]

Undefined / don't care states also allow for simpler physical implementations. For those whom did EE/CS undergrad might remember Karnaugh maps.