Rosh Hashana 13a - omer and chanukah

The gemara questions how the Jews were able to bring the korban omer when they first arrived in Eretz Yisroel. The Ran (in the chidushei haran) wonders why they couldn't have brought their own grain from the other side of the yardein, which would be kasher l'omer b'dieved. The Ran answers that even though something may be kasher b'dieved, the very first time you do something cannot be in a b'dieved fashion. Rav Yosef Engel (gilyonei hashas to Shabbos 21b as expounded by Rav Yonasan Sacks shlit"a) extends this idea as follows: the torah in Parshiyos Terumah/Tetzaveh tells us about the mitzvah of constructing the mishkan and its various keilim. It also mentions, along with each k'li, what that k'li was used for (the mitzvah of avoda associated with it). The gemara Sanhedrin daf 17 understands that while Moshe was able to consecrate keilim with the shemen hamishcha, once we no longer have the shemen hamishcha the avoda of the kli is what gives it its kedusha and allows it to be used in avoda. Essentially, the torah tells us of the avoda together with the construction because the completion of the "construction" may be the very first avoda one does with that kli. This is why the torah only mentions the korban tamid when it talks about the avoda of the mizbeach even though there are so many other korbanos for which the mizbeach is used (because the focus is not on what it is used for but on what its first use is for because it derives its kedusha and is only complete after the first use. The idea is that the beginning of everything sets the tone and must be on the highest level. The first use of each kli paves the way for every subsequent use and therefore is viewed with extra scrutiny. With this Rav Yosef Engel explains the necessity for the neis shemen on chanukah in light of tumah hutrah/dechuya betzibur. It may be okay to have the oil tamei for lighting the menorah, but it is not okay to have tamei oil for the chanukas hamenorah which is meant to set the tone for each subsequent lighting. This is why the ba'alei hatosafos on the torah explain "bi'krovai ekadeish" that on the day a kohein hedyot starts his avoda he can't become tamei even to kerovim, because the beginning and chinuch of his avoda must be b'tahara.