Sean Barrett (who I think popularized the idea) has a FAQ on this (https://github.com/nothings/stb) where he justifies it by pointing at difficulties with deploying libraries on Windows. Which is a fair point, but by going straight to header-only he skips the step where you can also just distribute a bunch of headers and .C files. The convenience of only having to include a single header is nice for quick weekend projects, but for anything bigger you're dealing with dependencies and build issues anyway.

I get some of the reasons that you would initially start out with a header-only implementation, but when your library grows, you probably want to split it at some point. For me personally, that point would be some time before the header reached 25k (!!) lines.