The manager should have the incentive to provide great feedback to the recruiter, as the recruiter will hopefully hit the target better on future candidates if they are aware why their candidates are being rejected. The recruiter has little incentive to share that feedback with candidates other than goodwill and keeping the relationship strong with the candidate. I always try to get feedback from managers for my own purposes and for helping my candidates improve, but it isn't always as easy as you'd think.
I continue to find that employers want a way to provide more feedback, though are currently prevented from doing so.
Someone with more insight into being a successful recruiter surely has a deeper understanding than mine, on this and other issues like the "numbers game" element.
I find it interesting that you find employers want to provide more feedback. A mere 30 seconds before writing this reply to your comment, I received an email from a client saying "We looked at the resume and don't think he is a fit for our team". That's it. If this manager wanted to help the candidate, he could mention what skills are missing. If the manager felt there was a problem with the resume, he could have mentioned that. If the manager wanted to help me hit the target better next time, he could have mentioned what was missing.
I think what you are referring to is feedback after interviews mainly, but this very bland, 'not a fit' feedback is exactly what is most commonly provided to recruiters. If given ample free time, managers will provide more detailed feedback, but that usually isn't the case (particularly in the start-up world). I do have clients that are more willing to write a few sentences, but I can tell you that the norm is 'not a fit'.
I don't find managers are in any hurry to help candidates do better next time, which does little to improve the overall ecosystem. If a candidate missed questions on a specific area in programming or a concept, that would be helpful for the candidate to know. I wish more managers wanted to provide more feedback, but for now it is a minority.