Why aqueous KI is used when collecting Iodine?
Your guess is right. Pure water does not dissolve iodine very well, but a solution of $\ce{KI}$ does, thanks to the formation of $\ce{I3-}$ and other polyiodide anions. And of course we would prefer to have our iodine in a dissolved form when we are going to titrate it.

When it comes to the starch reaction or redox reaction with thiosulfate, $\ce{I3-}$ is as good as $\ce{I2}$.

So it goes.