I don't really think this is 相槌; I tried searching here for "reflection" or "mirroring" as well but didn't find anything.
Let's take this example conversation:
A teacher suggested that by, adding the following, it becomes easier to understand (分かりやすくなる) but is not strictly necessary:
To me, this doesn't add any extra information and just duplicates the meaning of what was already there -- in fact, it's inappropriate in many situations, such as if B actually lives in Kyoto, and is planning on spending Golden Week in Tokyo in order to avoid crowds in Kyoto.
Does this phenomenon of reflecting back exactly the same phrasing that the questioner used have a name? And is it more important than in English? It just seems unnatural to me.
To put it another way, I'm having difficulty understanding why the teacher felt it was necessary to add this phrase to the conversation. All of the other edits on this assignment (which is about practicing the 〜んだから expression) are just corrections of simple grammatical errors, which makes this one stand out as I'm sure there's lots of ways my conversations could be rewritten that are left unstated when my work is corrected.