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?
There is absolutely no reason for std::deque to be a specification. The committee should either ship a committee library for std::deque or they should leave it to the community. They can provide a battery or they can not. Providing a spec for a battery that is both over and under specified is the absolute worst possible choice.
The standard library on the other hand is a library. It's almost always implemented as plain C++ without much platform specific code. ISO could take an existing free licensed implementation and declare it as the standard. Of course anyone is free to make their own competing one, it just has to always match the official library's behavior.
Writing a spec instead of code is just creating duplicate work and compatibility issues any time the spec is unclear.
Why on earth would I want a different implementation of std::deque on each platform I use because the compiler team needed to provide one? It’s madness!
I remember a language where the core language types, including primitives and a bunch of keywords, were actually defined in the standard library and the compiler just special cased support for the types in the standard library for optimization purposes.
Your loaded question feels very silly from that perspective.