No. The problem isn’t that std::regex is slow and badly designed. It’s that std::regex exists at all.
C++ is unique in that it defines a spec for STL but not implementation. The result is something that is both overspecified and underspecified.
Including batteries is fine. Including a spec for what the batteries should look like is such a profoundly bad idea that no other major language does it.
I'm confused about what exactly you're arguing for. Is the idea that the standard library should be minimal and then each compiler should ship its own nonstandard "batteries" library?