Obi-Wan vs. Anakin -- Why does he just walk away instead of finishing him off?

During the climactic battle between master and student, Anakin's legs are chopped off, after which he proceeds to catch on fire and begins burning alive. While it may seem safe to assume that a normal human would not survive such an ordeal, it's still incredibly illogical that Obi-Wan would, at this point, choose to merely turn and walk away. Instead of quickly confirming the kill, he decides to leave Anakin laying helplessly on the ground, but still breathing.

First, Anakin is NOT a normal human, but a powerful Jedi. Such Jedis typically seem to be able to withstand much more damage than the average guy. Perhaps more importantly, though, Obi-Wan and Anakin had a very close relationship--they were practically family. Even if Obi-Wan was in fact certain Anakin was finished, you'd think the master would still want to go over and quickly put his former Jedi "brother" out of his misery (via decapitation or whatever other means necessary).

Ultimately, the way the scene plays out is doubly nonsensical--Obi-Wan allowing Anakin to suffer a potentially slow, extremely painful death, while simultaneously (and foolishly) providing Anakin a chance to survive. Which of course he does.

I realize this is a common trope in movies, where the hero basically assumes the villain is dead instead of properly finishing him off. But it particularly stuck out to me here because of the multi-faceted silliness of the whole thing.

And yes, I also understand that Anakin needed to survive in order for the original Star Wars story to exist. Surely, though, the scene could have been written a bit less lazily and still found a way to produce the same outcome.

Then again, if I'm misinterpreting something here, please let me know.