Earlier quoted context omitted.
I despise the tactic of repeating back what other people said - it shows me that the other person isn't really dwelling on what I said, or more often in my experience, are using that to distort what I am saying in order to fit a particular agenda. I rather someone not fake listening in that case and wasting everyone's time.
I'm with you that repeating back word-for-word (or close to it) is not helpful. I think it's better to paraphrase back to the person talking; the closer the meaning of your paraphrase, the better it shows you've understood their point. Likewise with asking questions, if you can ask a relevant question that they haven't covered yet, it proves you're actually analyzing what they say. All of these things come under the…
I have found in the past that paraphrased repetition can be all the other person is looking for out of the conversation. A stylized sketch:
A: Hey, I have this problem XXXX, I'm not sure what I should do about it.
B: Ok, the problem is YYYY [paraphrased]?
A: Thanks, that was really helpful.