It might. There are at least two major things off the top of my head, regarding libstd:
1. specialization is needed for performance around String and &str
2. const generics are needed to support some trait implementations
We currently allow some stuff like this to leak through, in a sense, when we're sure that we're actually going to be making things stable someday. An alternative compiler could patch out 1, and accept slower code, but 2 would require way more effort.
There has been some discussion about trying to remove unstable features from the compiler itself, specifically to make it easier to contribute to, but it unlikely that it will be completely removed from the current implementation of libstd for some time.
> It's managed to build rustc from a source tarball, and use that rustc as stage0 for a full bootstrap pass. Even better, from my two full attempts, the resultant stage3 files have been binary identical to the same source archive built with the downloaded stage0.