I haven't been following Rust closely, so this is the first I've heard about the string/slice distinction. But I have spent a lot of time trying to remove unnecessary allocations/deallocations/copies from performance-critical, string-heavy C++ code. I use a combination of custom allocators and slice-like objects, but both of these approaches make it a hassle to interact with code using the natural std::string.

A pervasive distinction between strings that manage their own memory and those that don't, along with language and library support to make using them in combination straightforward would be a big win for me.