In the events of Chanukah, why did they need the miracle of the oil? After all, they did not need pure [Tahor] oil, as the Gemara says Tumah Hutrah beTzibur, meaning if everyone is Tumay then you can use tumay oil!
First of all, it's not so simple to say that "tum'ah hutrah betzibbur." There is in fact a halachic argument (Pesachim 77a, et al) as to whether it's "hutrah" (completely permitted) or only "dechuyah" (overridden); according to the latter view, tahor oil should still be used if possible. This is in fact the halachah (Rambam, Beis Habechirah 7:23 and Temidin Umusafin 3:10 passim).
Pnei Yehoshua (to Shabbos 21b) says that technically the miracle of the oil was not necessary, but that Hashem performed it to demonstrate that the Jewish People are precious to Him, and that their self-sacrifice in resisting the Hellenists deserved a special sign of His presence.
I have also once seen another answer (though I don't recall the source) that the rule of "dechuyah" or "hutrah" applies only when the sacrificial service was already being done daily. Here, though, where the menorah was being rededicated and relit for the first time in years (as indeed reflected in the name "Chanukah," dedication) - then that had to be done under conditions of taharah.