Growing up we always buried pets when they passed and the ritual was somewhat soothing. Digging the hole yourself was part of the final rite.
When my partners cat got euthanized she let the vet just walk away with the body for cremation and we got a little box of (hopefully the cats) ashes a few weeks later. Felt gross to me but she didn't want to touch the body and was fine having that sterile veterinary room be the last time she saw her.