Because there is no separation between API and implementation? Header files are great, you don't have to wade through implementation details or documentation to figure out what is API and what isn't, even more so with good use of pimpl. You hardly need separate documentation tools, because the header (when structured well) is just the signatures and documentation. Templates muddy this a bit, but you put those in .inl files and it all works conceptually very pure again.

Headers (or at least 'separate specification of API') are/is great, and I miss it dearly in other languages.