I have had a really bad body coordination, so I have had to learn everything the hard way. So I know A LOT of theory -- and over time, I have learned to coordinate my body much better. But some kinesthetic people are still naturals and move better than I do.
I agree with you that the major difference between dancing and other sports is probably not in the complexity of the movement. I think that the biggest difference is in improvisation and need to harmonize movement with your partner and music.
I also agree with you that there is almost no limit in either field on how detailed you can be in your body movements.
But even within weight training there appear to be various approaches, based on different goals. In my training, I almost never used 100 percent effort. Rather, the muscles were constantly stimulated with similar but different movements, all the time varying the stimulus. The muscles grow in rest.
It is very similar to how I have learned to dance. On the social dance floor, there are always limitations (such as other couples, tables, walls, music etc.) that come up. When you are improvising, you need to adjust your movements constantly (varying step length, direction, the movement you are doing etc.). And over time, you have experienced everything that can happen, and your body has learned to react to it, so "you" (i.e. your analytical mind) can relax and let the body move.
That said, when I was a beginner I used ”100 percent effort” a lot- because as a beginner my 100 percent effort was probably only really about 70 percent, I lacked the mental ability and pain tolerance for true 100 percent effort.
The majority of strength and cardio exercises are fairly simple to learn. Getting your form 100% correct is certainly more work, but generally not much.
Basic partner dancing can certainly seem fairly simple, but you very quickly move out of that and into the realm of most things being complicated. And even with the basics, if you actually focus on the technique, it's already a lot more complicated than most workout exercises.
I do expect that some forms of martial arts could be comparable (or perhaps even higher) in complexity to partner dance, though. But I'm not sure if I'd consider martial arts to be exercise as much as it's a sport or hobby.
(Source: former competitive ballroom and latin dancer.)
As the weight increases, it requires more focus to ensure that you are keeping your form and positioning and even just to engage your muscles `in the right way`. Form becomes more important/a pre-requisite in a way that ramps up as the weight increases as mistakes become harder to correct on-the-fly. The tolerances decrease and so the technique becomes more important.
It's not just your coordination and flexibility in placing legs, feet, arms, hands, torso in various positions at the right time, it's also leading your follower, adapting to their own abilities, tension, movement, mobility, and mood, connecting with them energetically, with the music, with the floor, and practicing dance floor awareness to avoid collisions with other dancers, adapt your moves to a rapidly shifting available dance space, and being creative and spontaneous.
With dance you need minimum 4 limb coordination (its more than this) to get started. You need rhythm and you need to memorize choreo.
At low weights lifting is pretty straightforward even for Olympic lifts. But your form only gets found out as you increase load and there's high risk of injury, and as you say you need a high focus.
As someone said - you chose the exception to the rule and the average person needs to use exercise machines because they lack the body awareness to even attempt strength sports.
That said the technical timing to strength sports is different to rhythm in dance/music. They both take focus but I think the brain is engaged differently. Especially as lifting is usually one movement and the movement is performed in a short burst. Whereas dance is a long sequence and usually a very different energy profile which is important. I do a lot of stuff but I recommend dance to people (as someone who doesn't really dance myself) because it forces you to relax in a way a lot of other exercise forms don't