Well, everything is in a header, so 'header only' is sorta correct - but the name is also problematic because that's what 'header only' C++ libraries (with the implementation in inline methods) are often called too, and those do actually suffer from downsides, such as increased compilation time.
A more correct name is 'STB-style single-file libraries' and it's really just a distribution format, nothing to get all worked up about - the differences to a single .h/.c pair are mostly negligible.
A common way to integrate such libraries into a non-trivial project is not to create one .c file for each header, but instead to create one .c file for a whole group of related headers (up to all external single-file dependencies of a project in a single implementation file), this may actually decrease compilation time the same way that unity/jumbo builds do, and since external dependencies don't change, this is also not a problem for incremental builds.
Another advantage: at least the original STB libraries (stb_image.h etc...) are often used in small command line tools, those can simply include the implementation in the "main.c" source, resulting in a project with dependencies that's still compiled as a single source file:
cc -O3 mytool.c -o mytool
...e.g. no build system needed at all.