This makes sense if you are writing an absolutely tiny library where the interface (the surface area) is a substantial fraction of the whole. In most projects of any appreciable scale, the user facing functions and types are a tiny, tiny fraction of the code and complexity of the whole. So no, this argument does not even come close to justifying using C instead of C++.
As few people seem to realize, it's common for even the C standard library to be implemented in C++. Having to implement all of the printf variants (there's 8, I think, at least) using C macros is horrible. Instead, the actual implementation of printf/fprintf etc happens in a function template. You then have one line extern C functions implemented via calling this template, which are declared in the header (and defined in the .cpp, along with the template).
As few people seem to realize, it's common for even the C standard library to be implemented in C++. Having to implement all of the printf variants (there's 8, I think, at least) using C macros is horrible. Instead, the actual implementation of printf/fprintf etc happens in a function template. You then have one line extern C functions implemented via calling this template, which are declared in the header (and defined in the .cpp, along with the template).