I agree. Plus the beloved pet appreciates it.
I had to put down a particularly beloved little friend, at age 16, diagnosed a year before with incurable feline squamous-cell carcinoma. She had been suffering for a while, but not so much that she didn't want to live anymore. The day came, however, when she "told me" she'd had enough. It was one of the hardest things I've ever had to bear. But i was there for her, and able to help her at the end of her life -- simply by loving her, and petting her, and speaking my love to her. And she let me know she appreciated it.
Yes, I had that happen also. When Peaches went, she just put her head in my hand and that was it.