Frank,
This is quite a can of worms, and I'm going to try to give you a very thorough answer, since I'm not exactly sure what you're asking.
I believe you're talking about the importance of maintaining full body contact while learning/working on dance technique. (Let me know how I'm doing here.) You also mention dancing with different ladies, presumably in social situations? One thing at a time, though...
I would say that for learning, teaching, practicing or gauging technique, body contact is usually helpful, rarely necessary, and sometimes detrimental. It all depends on your stage of learning, and what you're working on.
For a brand new student, for example, body contact will inhibit movement tremendously, and make learning to dance pretty darn hellish. I don't recommend it.
Once a student has learned some of the fundamentals of movement, body contact is not only the next natural part of technique to be learned, it is also an invaluable teaching tool. The additional communication inherant to body contact allows the teacher to feel what the student is doing wrong, and the student to feel what the teacher is doing right. Issues with the student's posture and movement are more thoroughly felt and better addressed.
Of course at the beginning, feeling everything more clearly usually means feeling uncomfortable in some way...separating and bumping into each other, tweaking posture, arching to maintain contact. There is tremendous value at times to using a practice hold, or normal dance position minus the body contact for working on quality and freedom of movement, swing, etc... Learning certain techniques with a freer connection, and then applying them in body contact can improve one's dancing (and therefore one's connection) immensely.
Now a quick discussion of how body contact is maintained. (This is relevant to the social dancing issue.) All points of contact should be fairly light, with enough tone to feel well connected, but not so much as to require any strain or tension, or to disturb your partner's position or balance. When in motion, body contact is maintained by both partners using the same leg and body speed, and moving their weight through each other. Body contact should not be maintained by hanging on to one's partner. This is so important it bears repeating. BODY CONTACT SHOULD NOT BE MAINTAINED BY HANGING ON TO ONE'S PARTNER! Therefore when social dancing, you can only have body contact if both partners take and maintain that position. If you don't have body contact, or close to it, it's probably not a good idea to do things like pivots.
Finally, while body contact is wonderful, and an integral part of really good dancing, it is by no means the most important element. To me, quality of movement is the most important thing...of course, good posture is integral to quality of movement, and once you have those two things you might as well throw in body contact...it's practically a natural result anyway. But I digress. Of course, body contact isn't the only interface or method of communication between partners...how about the hands, or the arm on the back, or even visual communication? I would much rather dance with someone who moved well, but in a more open position, than with someone who had a perfect full body contact dance position, but only moved halfway decently.
Okay, I've gone on too long already! Hope this helps. Correct me on the question if it doesn't. 
-Melissa
