My speculative reason: There seems no one have had the need compared to the efford to do it. I.e. you might be able to build an Eiffel Tower in your garden, assuming you have the space, the material, the people, the good enough ground, etc. and you can do it for your own pleasure. ;-)
The difference from C to C++ is as stated in the C++ standard:
In addition to the facilities provided by C, C++ provides additional data types, classes, templates, exceptions, namespaces, operator overloading, function name overloading, references, free store management operators, and additional library facilities.
If going to C++11, you might add lambda expressions and several other parts, all mainly syntactic sugar in the sense that they abstract something that is mainly parser related and could also be done (if not tedious) by other means.
What results as runtime items from parsing the above features are
- additional data types: some more built-in char/numeric types
- class: extended instance functions with
- class: inheritance with base class as sub object of a derived class
- class: special implicit function calls (ctor, dtor, etc.)
- class: vtable for virtual function calls
- class: ordering of definitions (mostly) do not matter in classes - only name lookup is affected
- templates: generated classes or functions based on type or constant integral values
- exceptions: additional control flow and especially cleanup-bookkeeping code
- namespaces: "syntactic sugar" (the unuique types, objects, fucntions get defined and called)
- overloading: "syntactic sugar" (the parser creates calls to the correct functions)
- references: "syntactic sugar", results in pointers or no runtime code at all
- new/delete: low level memory malloc/free plus ctor/dtor calls
- libraries: collection of items that base on language features
- lambda expression: "syntactic sugar" (implicit functor class)
There are nasty detail problems to overcome, but technically it can be regarded as a much extended C.
So, if you have a C++ frontend that manages to translate into functionally equivalent C, then you arrived at the level of CINT. Problems like multiple files and referencing libraries and object files is not unique to C++ but is a common fact with all C* languages. So, you can re-use these concepts of the interpreter of those languages (CINT?).
But again, justifying the effort depends very much on the prospective "gain".