Rashi, in today's Daf, Chullin 17, says that we need to know the status of besar nechira and besar ta'ava in the midbar, because although it's not nogeya anything, we need to know the truth. When is this the case, and when do you say, as the Gemara does in many places, mai dehava, hava?
Gershon
(a) The Rosh (1:23) rejects Rashi's explanation because of your question; if the Gemara recorded the question of Rebbi Yirmeyah, there must be a Halachic concern. (The Rosh therefore explains that the question of Rebbi Yirmeyah would apply if a person prohibited upon himself a particular food starting from a future date, and he had leftovers which he already had started eating when the date arrived. See Insights to the Daf.)
Tosfos seems to follow your approach as well. In numerous places (Chagigah 6b, Sanhedrin 15b) he asks why the Gemara discusses questions that pertain only to events of the past. He concludes that the Gemara does so when the discussion will help us better understand the verses written regarding the matter under discussion.
(b) Tosfos' premise (and your premise) is based on the Gemara in Yoma 5b, which questions the order in which Aharon and his sons first donned Bigdei Kehunah. The Gemara asks, "Mai d'Hava Hava!", and answers, "Lemisbar Kera'i" (i.e. we wanted to resolve seemingly contradictory verses).
I think that Rashi learned that Gemara differently. The Gemara's question there is, perhaps it makes no difference in what order the garments we worn. Who says that there was a particular order altogether! The Gemara answers, that the verses imply that there was an order.
The only other Gemara which uses the expression "Mai d'Hava Hava" in this sense is in Kesuvos 3a. There, however, the question is on an Amora who is clearly trying to create a Halachic distinction (regarding the days on which one may marry), and he obviously was not discussing past events.
Support for Rashi's approach to "Drush v'Kibel Sechar" can be found in Sotah 44a, where the Gemara seems to squarely place such discussion on the table of the Talmid Chacham - provided that he already learned all of the Halachic aspects of the Torah. (The Rosh and Tosfos probably agree to this, but they maintain that the Gemara would not codify what is just Drush v'Kibel Sechar.)
(c) A related issue is Hilchesa l'Mishicha. The Gemara only applies this argument to *Halachic rulings* that will only be applicable after the arrival of Mashi'ach (Zevachim 45a, Sanhedrin 51b - see Tosfos there), since Mashi'ach can rule for himself. If the teaching does not involve a Halachic ruling, we certainly may discuss it - since it has Halachic pertinence after Mashi'ach arrives.
Best wishes,
Mordecai Kornfeld