I don't disagree with you at all Richard. (Let me also say I am not a musician or performer, and I think that distinction can matter when it comes to singing or playing at the funerals or memorial services of family members or people or families to whom we otherwise had/have an emotional attachment.)

I managed to sing at my grandmother's funeral. I did break down some in the course of doing so, but within the context of that occasion, that was OK, and for the most of the song, I sang it well.   

My father recently died (making too many posts in reference to this, I know, but I've been around these parts long enough to be forgiven.) He and we had the luxury and the curse of forewarning.   He asked my remaining sister and I to sing a particular song at his memorial service.   We had to tell him we each knew we could not do it.   That was ok for him, and for us.

No regrets whatsoever regarding his memorial service. It was a perfect celebration of the life of my father.