What could C/C++ "lose" if they defined a standard ABI?

Question

The title says everything. I am talking about C/C++ specifically, because both consider this as "implementation issue". I think, defining a standard interface can ease building a module system on top of it, and many other good things.
What could C/C++ "lose" if they defined a standard ABI?

Answer 1

The freedom to implement things in the most natural way on each processor.

I imagine that c in particular has conforming implementations on more different architectures than any other language. Abiding by a ABI optimized for the currently common, high-end, general-purpose CPUs would require unnatural contortions on some the odder machines out there.