Same reason these same head hunters will usually strip any direct-contact details out of your resume before sending on to companies -- they don't want those companies running around them and contacting the candidate directly.
IMO, these people are all grifters and uses-car-salesman. Their goal is to get as many people as possible to use them to change jobs so they get bonuses. They provide little-to-no value add in the actual process and will actively try to shovel you toward shitty companies and dead-end roles, despite how well they dress them up.
You are ~20-50%~ cheaper (typical is 30% IIRC) in the first year of your employment if you are a direct hire instead of going through a recruiter, from a hiring manager's perspective. If you switch jobs often this compounds to make your offer chances lower as well if you're going through a head hunter (I've been part of these discussions from hiring side).