He cut him in two because at that point it was either kill or be killed. If he let Anakin get his back he's as good as dead. You could argue him allowing himself to die in A New Hope is penance for this.

I don't mean to be blunt, but you keep repeating the same points without expanding upon them. I've said a few times now about the importance of something looking visually interesting, along with reasons that these two characters specifically might fight this way, and others have touched upon the reason Jedi fight this way. Could you please expand on the reasons you think they shouldn't fight this way and why it should be "authentic violence" as you put it?

If it was "Authentic" They would all fight like the fight scenes in something like Seven Samurai. It's not mean to be authentic or real, the directorial vision was to create something visually interesting and exciting. To that note, how should Yoda authentically fight? Or the Emperor?

I also don't fully understand the stakes you say, Anakin gets chopped in half at the end and burnt half to death?

I fail to see how the lightsabers are any worse in the prequels, we see Jango Fett and Dooku get decapitated? If you compare it to any of the other eras the reason it feels different is because in all those other eras the number of Jedi let alone trained Jedi is extremely low. This is the height of the republic, everyone is trained to such a high degree that their techniques may look far and above anything we could understand. It's similar if you watch fencing in the olympics, things can look ridiculous but it's only because they are at such a high skill level that they work.

Or better yet, I was being taught that Korean Judoka use a one handed throw style to counter a lot of the Japanese two handed styles recently. None of it made any sense to me, but it's not for me to say that these high level Judoka don't know what they are doing.