A few of the respondents here talk about "they aren't zoos", and I believe they are right, however this is not black and white.
In my own case, as an owner who also interacts with my dogs as pets and companions, when a submissive is given to them it is an extension of a power and "erotic humiliation" AND of trust (going three ways, between she and I, my dog and I, and she and the dog). I'm not a zoo, I have no romantic interest in my dogs, which is not to say I don't love them....as pets and dogs and sometimes as a sentient, respected tool to use with those under my hand. BTW, that's a LOT more than I care about most people.
As for those who want to submit and add being "used" by a big male dog, start out as being a good human being first, they kind of submissive that I find appealing second, and establish that this type of kink is one of several areas you'd like to explore. This would take a considerable amount of time and effort. I would never just invite someone over for a puppy screw and then they walk away. In my experience this is an "Advanced Kink" along the physical and emotional lines of "Flying", or possible TPE where the Master (because you are way past "Dom" at that point) takes total control AND total responsibility for another human being. There are also the feelings of the dog to consider, you are training/conditioning an act that a dog really won't "Naturally" do (or if they do in some edge case, not on command and not more than once). As the owner/master, I've invested time in training them...and if the dog doesn't have the aptitude or drive, he's just not given that role. Some are retrievers, some are smugglers, and some are fuckers (and some aren't). They ARE all good boys!
So don't expect casual. Don't expect to keep a deception going for long enough to submit to an Alpha Dog master in my house. However, do the work on yourself to know what you need, where you want to go, and keep that interest in self-knowledge going as you learn through experience and relationships. Basically, be a good submissive in a genuine way, and maybe we'll get there.