From the Dom/me perspective (and I certainly can't speak for all Dom/mes), I do really and truly deep down want something close to complete submission from My Pet. Now, let me add a caveat: I want to be the ONLY person she submits to. I ADORE watching her tear apart rude people, idiots, closeminded jerks and the like. The last thing I would want to see is for her to become a snivelling, shrinking creature whose main purpose in life was to get kicked around by those close to her.
Also, My version of what "submission" is may differ a great deal from what you're thinking of as "submission", nawteeone. My version of "submission" is that I have the final say on anything W/we do as a couple and on anything she does short of things that would drastically affect her life. In other words, I don't want to control her work life (because I don't work, so I stand to lose a great deal by putting her livelihood in jeopardy), her medical life (because of her disability and because I simply don't know enough about it; I'm not a doctor) or her family life (because frankly, I just don't want them to know about O/our kink) in any way. What do I want to control? I want to be able to have her say to Me, "Here, can you call the Chinese food restaurant?" and to respond with, "No, that's your job" and be obeyed without question. I want to be able to, for example (if you've seen Secretary) tell her exactly how many peas she is allowed to eat on Tuesdays. I want her to know that I will collar her when she walks in the door and leave her collared until *I* feel the desire to remove the collar, and if she has to wear it in public, so be it. I want to know that she trusts Me so completely that she knows I would never intentionally harm her, physically or psychologically, and that because she knows this she doesn't fight back when I impose My will.
Frankly, while the "thrill of the chase" is sometimes fun, for Me personally that can get old extremely quickly. I find obedience and submission without prompting to be much more sensually pleasing and I'm more turned on by watching the switch in My Pet flip when she deals with Me as opposed to the rest of the world. I don't want to fight for her to submit to me; then I just feel like I'm making her do something she doesn't want to do.
Does that make sense?