Header files are an integral part of the language. Without header files, all static libraries, dynamic libraries, pretty much any pre-compiled library becomes useless. Header files also make it easier to document everything, and make it possible to look over a library/file's API without going over every single bit of code.
They also make it easier to organize your program. Yes, you have to be constantly switching from source to header, but they also allow you define internal and private APIs inside the implementations. For example:
MySource.h:
extern int my_library_entry_point(int api_to_use, ...);
MySource.c:
int private_function_that_CANNOT_be_public();
int my_library_entry_point(int api_to_use, ...){
// [...] Do stuff
}
int private_function_that_CANNOT_be_public() {
}
If you #include <MySource.h>
, then you get my_library_entry_point
.
If you #include <MySource.c>
, then you also get private_function_that_CANNOT_be_public
.
You see how that could be a very bad thing if you had a function to get a list of passwords, or a function which implemented your encryption algorithm, or a function that would expose the internals of an OS, or a function that overrode privileges, etc.