I suspect there are three main methods for increasing civility.
The first is what you suggest - some rigorous activity that pushes a person to learn their own and others’ limits. It doesn’t necessarily have to be physical. It could be intellectual, emotional, or even all three. The knowledge gained tends to make people humble, and humility leads to civility. However, that activity doesn’t require that a person be punched in the face or beaten into submission.
The second method is the development of empathy, a sorely needed trait in almost any gathering of humans. But there’s no real top-down way to nurture empathy in people except good parenting during childhood. If it doesn’t happen then, only the individual can decide to pursue it, and because empathy, by definition, requires enduring pain, most don’t opt for that.
The third method would be some severe, instant negative reaction to instances of incivility. Ostracism, condemnation, shaming. It’s possible to do these things while remaining civil, and certain parts of society have mastered the practice. But, it’s ugly, and it only occasionally leads to an individual rethinking their behavior.
To me, the real divide in behavior is the difference between anonymity and, if you will, onymity. In personal, real life discourse, there is instant feedback to incivility, and if the incivility is beyond the bounds of accepted behavior, that third method immediately comes into play. In the anonymous world of the Internet, there is very little recourse. I’ve yet to see a troll successfully shunned. Shaming and condemnation only appear to feed their behavior. Yet, you only have to check the news stories of some vitiolic iconoclast’s unmasking (for instance, the former Reddit editor) to see how the world comes crashing down on them when their real life identities are known.
There will always be anonymous areas on the Internet. They are too valuable and too useful to die. I do think that more and more interaction will require some manner of identification - like the “real name” reviews on Amazon. It would take a genuine sea change in human nature to make people more civil in an anonymous forum.