C++'s separation of spec from implementation is clearly functional. There are several major open-source standard library implementations that compete on the basis of performance, ABI stability over versions, quality, etc.

C++'s core ethos is "only pay for what you use". std::regex does this. In my experience, the "problem" with std::regex is that it provides more features by default than most people want, and you pay for using those features. Specifically, std::regex respects the runtime locale. There are good reasons a standard library feature might do this (e.g. it simplifies the interface, it's broadly applicable, etc.), but it's obviously not going to give optimal performance. This is a necessary tradeoff for any standard library.

Locale handling requires dynamic memory allocation, virtual function dispatch, sometimes system calls. Locale handling also prevents some low-level optimizations based on the character encoding. If you need that kind of performance, std::regex probably isn't for you, go grab a non-standard library that suits your needs.