Quote from Kahane-Was-Right BT
It is not "logical" that lighting a menorah is for a miracle. You are convinced that that is what it is for, so you are saying that is what it's for. There are multiple opinions about why we light, and even for those who say it's for a miracle of oil, there are different opinions about what the miracle itself was. I'm not disputing it or saying it didn't happen, but I am saying that it is omitted from ancient sources related to the land of Israel while the galut sources of later date (ie talmud bavli) stress this above all else. It makes sense to me that that is the galut approach and was very necessary and proper.
It is a little bit unfair on your insistence of pre-Talmud sources, because as you are fully aware of, until the days of Rabbi Yehuda Hanassi, all matters of the oral Torah, with a few exceptions were purposely not written down.
Oil miracles, also already appear in the Tanakh, where G-d helps the prophet Elisha to perform a miracle where one vessel of oil filled up many vessels of oil, in order to pay off the debts of a widow, who was about to lose all to her creditors. The Talmud in tractate Yoma, reports another oil miracle, in the days of the Cohen Gadol Shimon ben Shetach, that the oil in the western branch of the menora did not extinguish and the light kept on burning.
Oil miracles are not the sudden invention of the exile.
You ask, why then the stress on the oil miracle in the Talmud Bavli? Because the Talmud Bavli states, that the Rabbis wished to abolish all the holidays celebrating victories during the second Temple era, once the second Temple was destroyed. And indeed most of those holidays were abolished.
However, Chanuka and Purim were not abolished because there were mitzvas that were associated with those holidays and people would interpret abolition of those mitzvas as if Torah mitzvas were being abolished. Thus candlelighting, which was a minor element of the Chanuka celebration during the second Temple times,
Saved Chanuka from being abolished.
For a person living in the land of Israel, the element of being saved from the Greeks overshadowed other minor miracles, just as our salvation in the six-day war overshadows, the individual miracles that took place during the war.
But for someone who has lost all the elements of the national salvation, it is more appropriate for him to at least focus on the miracles of Chanuka, which have relevance even during the bad times of the exile.