Compilers are complex, platform specific and the architectures behind them can be wildly different. Maintaining a reference compiler would be a lot of work for no real benefit.

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.