I think I would rather do future "systems level" work in Rust than C, but I'm not sure it would eliminate the desire for automatic memory management in a casual or "ENTERPRISE!!!" (... no intelligent life here, Scottie) app :-)
I haven't used Rust enough to comment myself, but other people have said that Rust essentially does have "automatic" memory management (in the sense that you must manage the memory in order to get your program to compile). People say it works most of the time, at least. Rust is trying to make that as painless as possible, so it'll be interesting to see how painless it really is.