Exactly! And if an potential employer receives your CV from more than one headhunter, your CV will land into waste paper bin, because it is my easier than to clarify which headhunter gets fee and so on.
Moreover, a bad hadhunter (and 99% are bad) actually brings negative value. You, yourself can (and should) write a custom cover letter in context of the position you apply for.
But headhunter are laymen in your domain, i.e. I have experienced as they mess Java and JavaScript and are not aware that interest modeling and fixed income skills are essentially the same.
And last but not least, employers , ceteris paribus, always prefer the direct applicants because headhunter fees are not negligible (about 20% of annual wage is not uncommon) .