The singing is meant to mark time while the congregants say the prayers in the siddur. (On Shabbos, when those prayers are not said, the singing is omitted.) The Kohanim are trying to mainly stay together and keep a standard pace that will allow the congregation to finish, not put on a show. So if the singing sounds more functional than usual synagogue ...
I understand that not all Kohanim (or anyone else) have the most beautiful and melodious voices, but I believe that you are missing the whole point in focusing on this alone. It's the words and deed which matter most, not the voice they come from.
I have seen people pray and sing with the upmost beauty and fervor. Not because they possessed the voice of ...
I agree with @Aaron.
We should expect tuneful singing in Duchenen. But the kohanim have to learn the tunes.
The German-Jewish (Yekke) congregations have special tunes for each Yom Tov.
Here are two poor quality recordings of the tunes for Shovuos. IMHO the beauty of the first tune is still discernible.