This feature would IMO violate the contract that C allows you to specify memory layout of objects, to some level of detail (I am being a little vague about the “level of detail”).
Supporting closures, more or less, requires design decisions that are equivalent to choosing a specific layout for objects in an object-oriented language. C, as it is, makes none of these assumptions and you can translate a lot of different language ABIs into some C code (that may be clumsy). Keeping the abstraction that function pointers = pointers to entry points for functions, well, that’s frustrating for C programmers writing C programs, but extremely useful for interoperability.
At the moment we can not call nested functions or other things from other language from C, which is a pretty big hole in our interoperability story. I do not see why we need to make any design decision to specify object layout, we simply need a code pointer and static chain pair, which would then be sufficient to call arbitrary entities from other languages.