Why Moria?

[Zigûr]

Originally Posted by Inziladun

The idea was that of the Istari, only Gandalf had truly remained faithful to the original mission, which was the reason he figured so prominently in the story as written. Radagast did his bit in getting Gandalf to Isengard to bear witness to Saruman's treason. He then apparently went back to the woods to play with the rabbits.

I think this is a really crucial point. Radagast's role in the narrative of the Wizards is important in my opinion because it shows that the Wizards' failings didn't just involve becoming evil like Saruman - it could also mean becoming reclusive and apathetic. I think it's important that after sending Gwaihir to Orthanc Radagast disappears. Having another overtly heroic wizard like Gandalf would, I think lessen his impact and reduce some of the book's potential suggestions about the desperate situation of "good" in the world.
I think the rather curious remark that Radagast could not be located later on is one of those devastatingly subtle points Professor Tolkien makes so effectively in his writing.