I've never had one that did this (or told me about it, at least). My understanding was that the company is basically paying them to find talent, so you're the product being sold. Sometimes there's even a clause that if you quit too soon they have to give back their commission, which further incentivizes them to make sure you really are a good fit.
You don't pay someone less because they came via a recruiter because then they are going to be poached for being underpaid. You also don't pay someone more because they didn't come in via a recruiter otherwise now I have guys working on varying salaries which creates issues if that comes out in a team.
source: prior founder, hiring manager at large companies, etc
EDIT: based on the first reply I got I want to revise this slightly. Don't go into too much detail about who rejected you or how many times. In fact keep the details short but make it clear you think interviewing is a weakness they should coach you with
(Note that this only applies to recruiting agencies. A "recruiter" at the company you're interviewing for is the exact opposite story.)
Now that I think about it I'm not sure how to actually seek one out otherwise... you might attract them by putting buzzwords on your LinkedIn? It probably isn't too hard to Google for them either