Recruiter here. I think managers do have a careful balance between helping candidates (providing full disclosure as to why they rejected) and potential exposure (being sued or coming across the wrong way), so they tend to err on the side of caution. But having dealt with many managers, they too are in a time crunch, especially if they are being fed lots of unqualified or unvetted candidates (the numbers game you allude to) and also fear the risk. This is more prevalent in the contingency recruiting market.

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.