Now a bird/snake generally will be gone given the chance- but they truly are wild animals, while dogs are bred to be co-dependent with humans.
In addition the chances they want to escape are smaller than for birds. I looked it up and found this source https://www.petlink.net/blog/chance-dogs-coming-back-run-awa... that says "The unfortunate reality is that 15% of dogs across the United States go missing.". For context that's not 15% of dogs want to leave and do so. What's the percentage of dogs that had the chance to leave? Let's say 50%, which would imply that given the chance 1 in 3 dogs left. Albeit not all of the because they disliked their home/prison.
Looking at the language used in that article exposes some mental gymnastics. They simultaneously state that dogs could find their way back if they wanted and compare it to loosing a child! No, the dog is not a child, and if the reasons you provide why they "go missing" are "Fear from loud noises, Easy escape routes, Boredom and Prey drive" I find it hard to ignore that these are adult conscious beings that may not want to live with us, and only do so when given no alternative.
I wouldn’t be able to survive in the wild.
Some dog breeding is nonsense. But for the most part, we adapted to each other. If you look at the most efficient land predators, it’s humans, cats and dogs. (Dogs are also the only fellow persistence hunting mammals and, apart from some lizards, the only animals to practice it period [1].)
Our domestication of herbivores is exploitative. Our domestication of dogs and acceptance of cats is far closer to an alliance.
This is not true of any pet I’ve had. The dog was always gunning for an open door. And the cat enjoys unsupervised time outdoors when weather permits. They both always came home.
Also, cats aren’t truly domesticated. If there is a creature that “chooses” to live with us, it’s cats.
Our interaction with other life on this planet is very human centric, some call this human supremacism. A line is drawn between us and other animals, and the justification is quite arbitrary in my opinion. A line that is used to justify a vast number of atrocities and systemic exploitation. I don't believe there is no meaningful difference between a human and a cricket. But between a human and a dog or pig? That's close enough that I'm willing to extrapolate.