Why do domesticated animals enjoy and/or crave having their faces pet?
I’m pretty sure it replicates what mother animals do to their kin, which is they lick them affectionately. Our hands replicate this.
The maternal instinct of most animals is to nuzzle or lick their young to clean them and show comfort. The young creature learns to associate the sensation of being stroked or licked with feeling safe and warm and well fed. As adults these creatures still have this association so when we pet an animal on the head or stoke their fur in general it evokes these memories and feelings. So when we stroke a dog or cat it releases endorphins similar to what happens in a human when we are hugged.
To add to this young kittens have an instinct to press their paws into the mother cat in a massage style motion to stimulate the flow of milk. When an adult cat is happy and feeling loved it will repeat this massaging paws motion as it remembers the happy times of being a kitten and feeding from its mother.
Just my guess- it feels good. Even wild animals in temporary captivity seem to respond well to being scratched and petted.
Consider that our domesticated animals can’t generally reach their face. I just imagine we’re the only real way they can scratch an itch. But sure maybe it’s also related to how animals groom each other when friendly.
Also, for cats in particular, they have glands on their forehead that puts their smell on things that they rub their face up against, likely for marking territory. They seem to like having these areas rubbed in general, and it might be argued that they like marking people in this way
When we arent around, animals clean and snuggle each other very affectionately. Some people think the human pet mimicks moms licks, or the favor of grooming help, but it seems to me like they simply enjoy it just like the rest of us. Check out r/aww, even sea otters ask for scritches!