As far as I can tell, tzaraas is unlike other sources of impurity in that it is not impure until the Kohen says it's impure.
So why didn't the kohanim just not inspect the tzaraas, especially around the festivals (when impurity deprived people of the chance to do many mitzvot)?
And even if the kohanim did have a duty to search for the tzaraas, it seems to me that there would be no halachic problem if the person who might have tzaraas concealed it as much as possible. For instance, they could wear a bodysuit for the whole festival which covered every part of the skin except for the face.