This is a very loaded question, but I would like to work it out intellectually, please.
I would like to understand a basic premise of Rashi that reflects on my understanding of the transferring of the Oral Torah.
Basic statement (Kiddushin 33a, Eruvin 27a and more): "כל מצות עשה שהזמן גרמא אנשים חייבין ונשים פטורות ושלא הזמן גרמא אחד נשים ואחד אנשים חייבין". This is very common to use this kind of generalization, to say rules in the form "כל ..." or "כל ... חוץ מ-...".
The Gemorah brings R' Yochanan's own generalization on those generalizations (ibid): "אמר רבי יוחנן אין למידין מן הכללות ואפילו במקום שנאמר בו חוץ". The Pshat is that those generalizations cannot be taken literally as a rule, even if it includes "except for". The Rishonim and Achroynim discuss it extensively, but it does not relate to the question.
Rashi on R"Y says the following statement (ibid):
"אין למידין מן הכללות - כל היכא דתנן כלל לא אמרינן דוקא הוא
דאיכא כלל דלא דק במילתיה "
Every place where the [Tannoyim] Rabbis teach a [generalized] rule, we don't say "it is exact" as there are rules that a Tanna wasn't precise in his words (hope my translation is good).
I didn't see any interpreters arguing with Rashi on that statement and it is widely accepted as a rule of Mishnah. However the Rishonim and Achroynim do argue whether it applies to Amorayim and Rishonim and Achronim themselves, and the most agree (see Igros Moshe, brought in Metivtah in place) that it applies to all.
This is not the only place where Rashi and numerous others admit that the Rebbi and other Tannoyim chose imprecise or wrong wording, I am sure the readers are familiar with the phenomena.
What was the source the Tannayim relied on, to write their Mishnayot imprecisely - was it a tradition from Moses, if not, who started to be imprecise?
What are the reason and the benefits for teaching imprecise Mishnayot?