Rather a loaded question, and you seem to telegraph your thinking by using the term “subservient”, but I’ll bite.
Are domesticated dogs (sticking to a singular example) truly a part of their “family” of humans? While I am unaware of any research study on the topic, I can speak from anecdotal experience of some 60 years. Yes. They are part of their families. (Of course, it could be a relationship anywhere along the spectrum from intricately involved and mutually beneficial, to manipulative or abusive–not unlike the spectrum of all human relationships.)
Dogs have personalities, both individual and on the breed level. Some are highly devoted and loyal, others will go home with whomever appeals to them at the moment. They have their own individual likes and dislikes. Over tens of thousands of years, they’ve evolved and adapted to live within the human sphere. At the same time, humans have complex relationships with their animals, both to meet certain physical needs, as well as emotional support.
I have a Labrador Retriever (Woody) who is my constant companion. Because I am hearing impaired to some extent, he alerts me to movements and sounds of which I’d otherwise remain unaware, an invaluable service rendered when I’m out in the field at night doing moth research, or at home anticipating the UPS man. He’s there when I’m having a bad day, to keep me from staying inside my head to my own detriment. On good days, he’s a part of the family plans. In return, he gets two meals a day, three orthopedic memory foam beds, numerous toys, daily runs of at least three miles, and a considerable amount of fetch time. His medical care is a certainty, while mine is sometimes set to the side. I’m not an overly emotive individual, but we get along well. He’s one in a long line of companion animals I’ve had in my life.
Subservient? Let’s see. I get up in the morning, not when I want to, but when Woody does. My first action is not a cup of coffee, but to let him out, then feed him. When I would rather stay at my work in the afternoon, instead I am taking him out for his exercise, 365 days a year, regardless of the weather. I could buy something nice for myself, or a $20 allegedly indestructible toy for him–you can imagine who is the winner. When he tore his CCL, I drove 500 miles round trip to a veterinary surgeon and spent $4000 for the surgery. When he did it the second time, I researched alternative therapies rather than subject him to a repeat of the extensive pain and healing, spending hours, weeks, and months doing physical therapy, and he is now the picture of health. (And before you think I’m an isolated individual who focuses solely on her dog to the exclusion of anything else because she’s pathetically lonely, no. I’m married, the mother of four, grandmother of four, and rather busy.) All I ask from Woody in return is that he exist in my home and not pee on the carpet, or chew my shoes–neither of which he does. I suggest that I am the subservient individual if one must be designated so.
I’m not alone. Any veterinarian can attest to the depth of relationship people can have with their animals, and the extent to which both thrive because of it.
The subtext here seems to be the suggestion that it is time to end this relationship; I think it’s a little late to stuff that one back in the bottle, unless someone is suggesting we summarily render every domestic dog on the face of the planet sterile and allow them to die out. To allow them to revert to a feral population is patently absurd and would be cruelty in its highest form.