Why are ground wires sometimes not insulated?
Cost, mostly
Whether your grounding conductors are bare, insulated, or not even a wire to begin with depends on what wiring method you are working with.  NM, because it's made in large quantities, uses a bare grounding wire to save cost (likewise with UF and most SE cables, as those pennies add up at industrial scales).  On the other hand, if your house is wired using armored cable (AC), there are no ground wires, because the metal cable armor serves as the ground with the aid of a thin &quot;bonding strip&quot; to prevent &quot;choking&quot; of fault currents caused by stray inductive interactions.  That lack of grounding wires is also a notable feature of many installs done in metal conduit, as the conduit itself then becomes the grounding conductor.
Furthermore, some wiring methods aren't uniform in how they handle this; it's legal (and occasionally required) to run a separate equipment grounding conductor in metal conduit, and in most (albeit not all!) cases, equipment grounding conductors inside conduits can be either bare or insulated.  Likewise, metal-clad cable usually uses an insulated grounding conductor, but can sometimes be found with a bare grounding conductor, or in configurations where the armor is the grounding means.