Rabbi David Shamula answers...
In Parshat Emor 21:6, the Torah states regarding the Kohanim, "they shall be holy." The Gemara (Sanhedrin 51a) teaches, "this includes those Kohanim who have a blemish." We learn from here that even though Kohanim with a blemish can not offer up sacrifices, they are still considered holy. But what is the source of their holiness?

In 21:1, the Torah prohibits the "sons of Aaron" to become impure by coming in contact with a corpse. Torat Kohanim teaches that "sons of Aaron" include those who have a blemish. Just being of the sons of Aaron gives them a special holiness, which sets them aside from the rest of the Jewish nation (Kli Yakar.)

(For further study see Sefer Hachinuch, Emor, Mitzvah 273 and Kli Yakar, beginning of Emor, for the reasons the Kohanim are forbidden to marry certain women and become impure to a corpse.)

These prohibitions apply nowadays even though we don't have a Beit HaMikdash, because their holiness stems from their being the sons of Aaron, regardless of their eligibility to serve in the Beit HaMikdash.

Furthermore, the Torah prohibits Kohanim who have already been defiled from again coming into contact with the dead. This would actually increase their level of impurity (Torat Kohanim 21:3, T.B. Nazir 42, Masechet Smachot 4, Rambam, Mourning 2:15, Shulchan Aruch and Rema Y.D. 373:7.) How is this illustrated?

Someone who is connected to a corpse has an impurity level of Avi Avot (1st level of impurity), which would make anyone who touches him at that time an Av HaTuma (2nd level). But once he has detached himself from the corpse he is downgraded to an Av HaTuma which would make anyone who touches him Rishon LaTuma (3rd level). A Kohen is prohibited from any further contact with a corpse which would again make him an Avi Avot.

Thus Kohanim in the present day, even though it can be assumed they have become impure by contact with corpses and therefore are Av Hatumah, are nevertheless prohibited to defile themselves further to the level of Avi Avot HaTuma.