Definitely not an idea way of getting candidates - you are selecting for people who know how to manipulate screens (and thus increasing the risk of getting a bad candidate), or rejecting otherwise knowledgeable people who just don't have the time/inclination/"social savvy" to pretend to be stupid.
If you can't figure out that the first person who's interviewing you has answers on a sheet of paper and you're supposed to parrot them until you get to the second person, how are you ever going to figure out that the first person you're selling to has some business requirements on a sheet of paper and you'll never get to the second person until you parrot those?
"Oh, we're not actually using Docker, we're using rkt, which is a compatible reimplementation of --" "I'm sorry, I've been told Docker is a requirement. We can't use your Cuber Netty thing until you support it. Bye!"
If it were me, I'd try to engage with the recruiter and make them go completely off book. I'd ask them about their career, and try to find a different job for them (instead of reading stuff off a sheet of paper), or if that's what they are content to do, try to escalate and get them to reveal their "client" or "person they report to" (which in recuiting is a no-no) - I think I have the confidence and social skills to try to do that (I've talked past border officials, and various recruiters, and having been in a tele-job where I had to follow a script, I know exactly where a script reader is most likely to go off book if I ask something at exactly the right time). I am in no way qualified for a director of engineering position, but I can very easily get past this telephone screening, because precisely I've been the person asking this kind of question and using this kind of script. If I got past this screening, I'd be wasting the time of the person next in line for the interview.
Of course, it is a valid strategy to get an interviewee to follow along, but it's misguided - using the entirely wrong tool (scripted questions/answers) for doing the job (finding someone with managerial and people talent).