To answer the question "Can't we just work out because it feels good?"
No, we can't. Some people can, many, if not most people, can't.
I am self-driven, been devising my own workouts and targets for decades, was certified as a trainer, and have taken almost no classes, except for ballet one semester, but I acknowledge that many people require some social aspect to their routines, either a friend, a trainer, or a class. Even more so, we all have different sets of goals. For some, getting healthy is fine, but some are competitive, some are athletic, some like novelty, while others like routine.
People are different.#2:
It seems many commenters are hostile to these people, berating class-takers' ambition, describing them with a variety negative terms. Some might see these people as narcissistic and overly competitive, but they might be driven, and either new to fitness or people looking to push their limits after finding themselves bored. The class format gives some people a way to strive without being 'jerks' to their fellow humans.
I've been working out for 27 years, mostly on my own, was certified as a trainer over 20 years ago, and was a member of a competitive rowing club in my late 20's and early 30's. I found the rowing club atmosphere, as well as club competitions, as a way to push myself harder, without having to be directly competitive. Now, at 55, I aim for the gym four (4) times per week, and engage in either rowing machine or spin bike workouts, but there were periods where I was driven to improve and aimed for beating the curve, and group activities helped me do that.#3:
Not taking anything away from your fun, but some of us like hard work, the rewards and the feeling of accomplishment, and that is a kind of pleasure. The most rewarding activity for me was rowing - I still use the machines several times a week - something that often has people responding that it is a hard. To be honest, I love the visceral aspects of rowing while listening to my favorite rock/metal/dance music, again, another pleasure.#4:
You obviously aren't considering the pressures and concerns of women. While strength and muscle might be perfectly healthy, and socially acceptable if you are a man, for women, and in particular, smart, ambitious women, you live with a different set of concerns, which although it comprises fitness, health and strength, it also covers social expectations about beauty and appropriate behavior.