Frankly, the Shikkerdovid is always a little uneasy when it comes to talking about cohamim. It is such an arbitrary distinction. Piety is not inherited and neither shouls priesthood. This thought or concept kind of wends it way into the beginning of the parsha and the Ramban. The Parsha opens with the menorah. Rashi asks why is the Menorah mentioned after the princely gifts. His famous answer is that Aharon was said watching everyone bringing gifts and he didnt. Therefore, Gd gives him the mitzva of the Menorah.
Ramban argues. Now frankly Shikkerdovid dosent really entirely understand all the language of ramnban, but here is the gist and lesson. Ramban says, that Ahraon had plenty of things to do, sacrifices, Yom kippur etc. Why mention this thing in relation to the princes. His answer is that the Hasmoneans (priets) will be the star of the Hanuhah story and the menorah will be light by them and saved by them. Furthermore, and even after the holy temple stands, this mitzva will continue in the form of Hanukah.
Here is the irony. We still light the Chanduka candles. We all light the Chanuka candles- Not just cohanim. The other mitzvot of the temple are lost. This one survives-albeit for one week and certainly to commorate a historical event. Here is MAYBE the lesson. Truly holy acts are timeless and not relegated to specfici people. They continue by all people.