This is terrible, but I read this and my mind switches back to nerd stuff: how great would it be if software developers could hire someone like this but to handle job outreach and negotiation? You: kick back, solve programming puzzles, go to the occasional tech-out interview. They: reach out to prospects, arrange your interviews, and do the salary negotiation.
They're really different skills, programming and job negotiation. They're not even correlated! I know so many excellent negotiators with excellent jobs who aren't even in the top 50% of programmers I've worked with, and vice versa.
I suppose it's probably similar with dating; being a good partner probably has little to do with being good at arranging dates.
Later
Heading off a bunch of replies right here:
Recruiters work for hiring firms. How you know this is, developers don't generally pay recruiters. The essence of an agent/principal relationship is that the agent works for, and is compensated by, the principal. Recruiters aren't talent agents for developers.