One of the worst I've experienced had a bug where adding too many files would cause intermittent errors. The people affected resorted to header-izing things. Was an off-by-one in how it was constructing arguments to subshells, causing characters to occasionally drop.
But, more commonly I've seen that it's just easier to not need to add C files at all. Add a single include path and you can avoid the annoyances of vendoring dependencies, tracking upstream updates, handling separate linkage, object files, output paths, ABIs, and all the rest. Something like Cargo does all of this for you, which is why people prefer it to calling rustc directly.
People certainly sometimes create a horrible mess. I just do not see that this is a good reason to dumb everything down. With a proper .c/.h split there are many advantages, and in the worst case you could still design it in a way that it is possible "#include" the .c file.
I tried to use cargo in the past and found it very bad compared to apt / apt-get (even when ignoring that it is a supply-chain disaster), essentially the same mess as npm or pip. Some python packages certainly wasted far more time of my life than all dependencies for C projects I ever had deal with combined.
I consider it compiler abuse to #include a source file. Useful for IOCCC competitions though.
Apt is fine for local development, but it's a bit of a disaster for portability and reproducibility. Not uncommon to see a project where the dependencies either have unspecified versions whose latest versions in universe are incompatible, or where the package has been renamed and so you have to search around to find the new name. Plus package name conventions are terrible. libbenchmark-dev, libgoogle-perftools-dev, and libgtest-dev are all library packages from the same company. The second one is renamed to gperftools-lib with RPM repos, to further compound the inconsistency.
I find myself dealing with package and versioning rename issues regularly in the CI pipelines I have using apt.
Well, I consider it abuse of header files to put an implementation in there. And comparing including a c-file to IOCCC seems very exaggerated.
My experience with dependencies in Debian-derived distributions is actually very good, far less problematic than any other packaging system I ever used. But yes, one needs to maintain dependencies separately for RPM and others distributions. But obviously the problem is not lack of a package manager and adding another one would not solve anyhing: https://xkcd.com/927/ The solution would be standardizing package names and versions across distributions.
But, more commonly I've seen that it's just easier to not need to add C files at all. Add a single include path and you can avoid the annoyances of vendoring dependencies, tracking upstream updates, handling separate linkage, object files, output paths, ABIs, and all the rest. Something like Cargo does all of this for you, which is why people prefer it to calling rustc directly.