Why use potassium iodide instead of copper iodide in Sandmeyer reaction?

The Sandmeyer reaction is an extremely useful reaction for the functionalization of aromatic rings through a diazonium intermediate. For conversion of a diazonium intermediate to the corresponding chloride, bromide, or cyanide, the copper(I) salt is used. Surprisingly (to me at least) for iodination, potassium iodide is the reagent of choice, as described in Maitland Jones's Organic Chemistry (and elsewhere I'm sure), but no rationale is given. SciFinder searches also show that potassium iodide is most frequently used.

Is there something special about copper(I) iodide that makes it unsuitable for use in the Sandmeyer reaction?