The Torah lists many types of blemishes that render a Kohen impure to bring a Korban. The question arises as to why physical defects make a Kohen Pasul from bringing a Korban if it does not seem to affect anything spiritually. Rabbi Elie Munk cites a range of answers to this question:
Rashi quotes Malachi who challenges the people to bring blemished and crippled animals to their Ruler as a gift and see how He likes it. Rashi deduces from here that just as bringing blemished animals shows a lack of respect, the same principle would apply if the foremost servants in the Bait Hamikdash had a blemish.
In contrast to Rashi, the Rambam focuses on the perspective of the people and not on God. He says that public opinion judges a man not based on his true value but on the perfection of his limbs and the beauty of his clothing. If the Kohen as unblemished, it would ensure that the Bait Hamikdash would be revered by all. It is for this reason that the Leviim would be allowed to work in the Bait Hamikdash if they had the same defects that would render a Kohen Pasul. They did not offer sacrifices and were not considered agents in asking forgiveness for sins. Rather, they provide vocal music and therefore were rendered Pasul only if they lost their voice.
Ramban differs from the rationalist approach of the Rambam and says that a Kohen is Pasul if he has physical defects only because it is a reflection of the spiritual defects he may have.