From my experience in DE, it depends on the company size. Larger enterprises probably will go through an agency, probably to (try to) cover themselves against accusations of false self-employment (Scheinselbstständigkeit).
Anecdotally, the two contracts I had through agencies were still the most lucrative financially, despite the middleman taking a hefty cut, simply because large enterprise pay higher rates.
Anecdotally, the two contracts I had through agencies were still the most lucrative financially, despite the middleman taking a hefty cut, simply because large enterprise pay higher rates.