For general purpose sort like std::sort & std::stable_sort the obviously faster (and of course safer) choices are the Rust equivalents [T]::unstable_sort and [T]::sort and their accompanying suite of functions like sort_by_key and select_nth_unstable
There is movement towards adopting the same approach for C++ by some vendors. The biggest problem is that there's a lot of crap C++ out there buried in erroneous custom comparators and so if you change how sorting works even very slightly you blow up lots of fragile nonsense written in C++ and from their point of view you broke their software even though what happened is they wrote nonsense. Next biggest problem is that C++ named their unstable sort "sort" so sometimes people needed a stable sort and they got an unstable sort but in their test suites everything checked out by chance, and with a new algorithm now the test blows up because it's an unstable sort...
There is movement towards adopting the same approach for C++ by some vendors. The biggest problem is that there's a lot of crap C++ out there buried in erroneous custom comparators and so if you change how sorting works even very slightly you blow up lots of fragile nonsense written in C++ and from their point of view you broke their software even though what happened is they wrote nonsense. Next biggest problem is that C++ named their unstable sort "sort" so sometimes people needed a stable sort and they got an unstable sort but in their test suites everything checked out by chance, and with a new algorithm now the test blows up because it's an unstable sort...