And notably, C++11 actually moves in this direction, standardizing things like smart pointers [0][1]. It's a very smart move for Rust. Core or near-core library wars in the early days of adoption of a language leads to duplication of effort, and for those invested in seeing Rust gain a set of libraries to rival other languages, this is a great thing.
Actually, C++'s STL is in a weird situation, compared to the standard library in other languages, because the STL is a spec, not an implementation. And there are as many implementations of the STL as there are compilers. This might arguably happen if there were multiple Rust compilers, though. Anyways, the result on the C++ STL is that in many cases, the same types have different performance characteristics on different platforms, or worse, different behavior/bugs.
[0] https://en.wikipedia.org/wiki/C%2B%2B11#C.2B.2B_standard_lib...
[1] https://en.wikipedia.org/wiki/Smart_pointer#unique_ptr