She didn't kill him cuz she felt he needed to think over the life he's lived.
As far as Arya and the Hound death scene is concerned, I'm just going to forget the books (don't read 'em, but hear reveals). I felt she was so stoic and quiet during that scene because she wanted to know what he'd say, how he'd respond knowing (or thinking he knows) that he was dying.
To me, it's a sort of confession scene, though you have to read between the lines. He admits his lifelong loneliness, but ultimately is not a bad man.
Arya is becoming quit cold and ruthless. Like Anakin, she may be walking down the Dark Side. I do think all of her killings so far have been justified. Though this thing with making The Hound suffer is odd. He did kill the Butcher boy, which is why he was on her kill list, but I think she's forgiven him for that. If not, that's part of the reason she's letting him die slow, because c'mon, how's he getting out of this?
I think Arya not killing the Hound is also reflective of the lessons she learned from another kill they had along their journey. That of the old man that Arya and the Hound comes across, severely wounded by the raid, and dying, and the Hound does the merciful thing, giving him his last drop of water, and then killing him, ending his pain.
I think Arya, although she begrudgingly accepts the Hound as a person, and that he's not all bad, still is not completely convinced that he deserves mercy, a merciful death. Justice versus mercy. Imagining that they lie on the opposite ends of a continuum/spectrum.
Getting to know him along their journey, the clear lines between Justice versus Mercy, with regards to the Hound, blurs for her. So, she detaches herself, and leaves him to his own fate.
Justice, as she had initially promised to carry out, would be to kill him for killing the butcher's boy, on her terms, not his, when he's not
wanting death, but she gives it to him, regardless, thereby delivering justice. Hence, why he made it to her (s)hit list. However, as time went out, I think she started to falter from that conviction of delivering Justice, with regards to the Hound.
However, she also saw examples of mercy, a merciful death, and, I don't think she was there yet, to jump from one end of the spectrum of Justice, all the way to the other end, towards believing that the Hound deserved a merciful death.
In Arya's eyes, he might no longer deserve the death she planned to carry out, in the name of Justice, but that doesn't mean he automatically makes it to the complete opposite end of the spectrum, towards yet deserving mercy. Morality, as GoT points out, is rarely black and white, and the journey from Justice to mercy is not one step over, but a process.
So she leaves the decision, the situation, where the colliding conclusion between justice and mercy, in that case, could have been one and the same. Hound's death. However, the delivery of it must be what defines justice from mercy. And, as this case wouldn't allow that distinction between delivery: would it be justice? would it mercy? She gave him neither.
He can't walk, the only living people within like 100 miles seems to be Brienne and Big-Dick boy.
LOL, that's Pod's secret with the ladies, is it?