I’m glad for you and your cat but the question was, do hospitals even allow that now?
We mourned and funeralized our cat this way last week.
As for humans, they do have ways to release the body to the family. I have friends who have had funerals for stillborn children over the past several years.
It's a much loved and anticipated family member, not a hunk of biowaste.
From the article:
Most states legally require only a certified death certificate, a permit giving permission to transport the body for disposition, and that the body be buried, cremated or donated to medical science, Slocum says. Theres no law that says you have to have a viewing. No law that says you have to have an embalming.