A comment from the author /u/ClayTownR on reddit:
The original reason I got into garbage collectors (a long time ago, and long forgotten now) was that I was implementing a runtime for a scripted language. When I originally wrote it, I had to do some manual finagling with weak references to ensure that I didn't leak any memory.
In general, the main uses for a GC in rust would be interpreters for other GC languages and working with graphs.