Defilement of a Kohen for a Relative without Necessity

A Kohen who is commanded to become impure for his relative, is he required to do so only for the burial, or even without necessity?

According to the Shulchan Aruch, it is a mitzvah to become impure even without necessity for the deceased, but according to the Rema, it is proper to be stringent and become impure only for the purpose of burial and to bring him a coffin and shrouds. However, being near the Chevra Kadisha while they are attending to him is considered necessary since they might need something from him. And once it is necessary to be there for the deceased, one may remain.

According to the Ramban, defilement occurs both with necessity and without it, but according to Tosafot in Pesachim 9a, a Kohen becomes impure only when necessary. Halacha: Shulchan Aruch, Yoreh De'ah, Siman 373, Sif 5: "All those for whom he becomes impure, even without necessity. Some say only when necessary." Thus, the ruling in general and particular, like the Ramban, that it is permitted to become impure without necessity. However, the Rema wrote there: "And it is proper to be stringent according to the latter opinion, not to become impure except for burial and to bring him a coffin and shrouds." And in the Shach on NKK, it is written that the main opinion is like the first. Pitchei Teshuva, Yoreh De'ah, Siman 373, SK 4: "The Gaon of Lissa wrote in his prayer book that on weekdays it is permitted to be in the house of the deceased, as it is a mitzvah to become impure for him, even if others are engaged with him, one still needs to be there, as it is possible that something will be needed for the coffin and shrouds and similar, this is considered necessary for burial and it is permitted to be there." See Minchat Chinuch, Mitzvah 264, where this discussion is linked to the question of whether impurity is permitted for defiling relatives or deferred. From the words of the Rema, it appears that according to Tosafot, one should not become impure for guarding and honoring the deceased, and therefore a Kohen should not become impure to cover his father's eyes with earth. However, in Minchat Chinuch, it is written that even according to Tosafot, it is permitted to become impure for guarding and honoring, and all that is forbidden is to see whether he is male or female, as this is not necessary for the deceased.