It only takes one time being surprised.
It’s always a risk. Would you want your best friend to go into a polar bear enclosure alone even if the bear had never mauled anyone or acted like it wanted to?
It’s never worth the risk if you value the little bird’s life.
What happens when the bird lands on the dog’s eyes and scratches it? How confident are you that the dog won’t give a warning nip?
Furthermore, mammal saliva is toxic to birds. This is stupid in more ways than one.