Ah, but that's where you're wrong. Going cheek to cheek is a lot like going toe to toe. There's the close quarters, obviously, something any fighter has to get comfortable with. Thanks to the improvisational nature of most dances, you're also going to fine-tune your awareness of your partner's movements so that you can respond intuitively in real time. Dancing in a
close embrace heightens the intuitive aspect even further because you don't even have a visual on what your partner is doing. It forces you to move by feel.
Most ballroom get-togethers rotate each dance throughout the course of the evening - you'll do a foxtrot, a salsa, a nightclub, a waltz, a tango, etc one after the other. No rule says you have to do them all, but who wants to be a wallflower? A big martial benefit of this of course is that it forces you to be flexible in your thinking. If you can wrap your mind around ten different types of footwork every hour you'll be less likely to catch yourself repeating unhelpful movements in a crisis situation. Imagine a parallel situation in martial arts - what if people in tournaments were expected to show their competence in several arts over the course of a day? I suspect we'd have a lot more mutual respect among all the arts, and a lot more renaissance fighters.
As with any MA class, the highly social nature of dancing encourages people to dance with several different partners, usually a different person for each song. As with MA, dancers get used to working with a huge variety of different body types and movement styles. That skill is critical to success for practicing any martial art. And if you're wearing high heels, you have the added training benefit of having every step you take being on uneven ground.
And while it's not supposed to happen, I've actually had the opportunity to cross the line into MA right there on the dance floor. At one of my favorite dances I've noticed the female population dwindling. When I asked around, it seems that there have been a couple of new guys with sticky fingers (oh, was that your ***? Sorry, my hand must have slipped.) I haven't had the pleasure myself yet, but I'm thinking about getting a little clumsy myself (oh, was that your instep?
Darn these stiletto heels!) I haven't actually done it, but I'm not ruling it out either if I find myself in the arms of a total douchebag.
Dancing is one hell of a workout too. Martial artists need stamina and strength, whether it comes from weights, jogging, swimming, or the rumba. Movement is movement is movement. It's all in the intention.