Firmly tongue-in-cheek, I would say that if a competitive couple found it impossible to do any of the standard dances at a social dance, then they have not actually learned to dance, but merely to repeat sequences of steps which they have practised on an empty floor. For me, that isn't dancing, it is indulging in the luxury of being able to present your most advanced technique, or most advanced figures (and preferably both), without the inconveniences and limitations of being one of a hundred dancers on a busy floor.
Dancing is about leading and following, floorcraft, and the pleasure of one's partner's company. It is also about technique, expression and the appropriate selection of figures (but choreography is really limited to the demonstration/competition scene). Dancesport uses a sub-set of those skills, with some of them developed more highly, but at the expense of others. I would say (and still firmly tongue-in-cheek) that the "compleat" dancer would be as comfortable on a social floor as anywhere else, and if they really did have to keep stopping and starting, then they really should have stayed at home, and had a night in to re-read Alex Moore.
At our social dancing club, one couple regularly attend who are, principally, competitive dancers. They also happen to be very good (and the two are not the same thing at all). On a busy floor, they enjoy the quite different challenge of dancing within the limitations of those figures that can be executed in the available space, without undue inconvenience to themselves or to anyone else, and they will also regularly partner other, less experienced dancers too. They usually confine themselves to basic figures, executed with the sort of style and expression which means that they can be spotted from the other side of a busy floor instantly: everyone's eyes are drawn to them, because their dancing is so attractive. Nothing stops ANY social dancer from doing that!
The two groups are, in reality, chalk and cheese. Most often, the social dancers are content with a very modest standard, and being content, they are just enjoying themselves; while the competitors are striving for improvement, and pushing the boundaries of their own dancing all the time. Mostly they fail: only one couple win each comp., and lots of dancers are eliminated in the first round.
There is always enough room to "perform" a stylish closed change, natural turn, closed change, reverse turn, whisk and chasse routine in standard waltz on a busy floor, and anyone who couldn't do it is kidding themselves that they are a dancer - even if they have a shelf full of trophies and are being coached by someone who could!
As for the non-travelling Latin dances - things are much more even as between the two styles, which are more or less interchangeable between the competition and social dance floor. Probably the only adjustment needed is for arm extensions to be predominantly upward socially, rather than outward (we don't want to knock anyone's teeth out), and then everything is fine. Samba is not usually so popular on the social floor, so there is usually more room to move, but we might have to be ready to make adjustments, but nothing major; and of course, paso doble is hardly danced socially at all, needing as it does, the choreographed approach to the telling of its story.