Is there any specific reason why we should prefer a module system as it exists in C++ over something like the SQLite's approach with Makeheaders[1]?

As far as I understand it, they have a tool that can parse all their (C) files, figure out what each file declares and what declarations it depends on, and then autogenerate a header for every file with just the declarations it requires.

It seems like a sensible approach, but nobody besides sQLite and Fossil (which comes from the same developers) seems to be using it, either in C or C++, which leads me to suspect that there are caveats I don't know about. Is there a reason why this is a bad idea?

[1] https://fossil-scm.org/home/doc/trunk/tools/makeheaders.html