I think this is an unnecessarily cynical view. A phone call is just warmer, and recruiters probably close more often by going to a phone call.
In almost 100% of the cases, if a Recruiter is able to get someone a job, it's immensely beneficial to the new employee, far more so than for the recruiter.
Up-thread they said they explicitly asked for email instead after taking the cold-call. What's the good faith reason for insisting on a warm phone call when it's not wanted?