regeneration - Why does the War Doctor regenerate?

It's his reward isn't it?

At the beginning of the story the Doctor Hurt tells Rose/Bad Wolf/Moment -

"I have no desire to survive this" and she/it replies "Then that's your punishment, if you do this, if you kill them all, then that's the consequence: You live."

Given that this specifically refers to the destruction of Gallifrey ("... killing them all, Daleks and Time Lords alike" as she/it says) and he doesn't do it, then logically he shouldn't be punished, so should die rather than live.

Thus he doesn't have to continue being the Doctor who fought in the Time War, but can be a new man who can put some distance between himself and the other things he did in that War ("I've been fighting this War a long time; I've lost the right to be the Doctor," he says.)

Of course, it's a bit double-edged, because the Eccleston Doctor is a bi-polar PTSD sufferer who thinks he's committed double genocide (due to not being able to "remember that I tried to save Gallifrey rather than burn it") and it takes a second Bad Wolf induced regeneration (in The Parting of the Ways) to allow him to get over that.

Outwith the fiction, I suspect it comes from a combination of the fact that we know this story was conceived (Moffat has said as much in DWM) with Eccleston's Doctor in the Doctor Hurt role (and thus there was no regeneration at the end originally) and a desire from the production team to 'cap off' the War Doctor with a regeneration scene. After all, Moffat has spoke of his own fannish desire to see McGann regenerate, surely the same impulse applies? It means that what happens is thematic rather than strictly plot-based, but it does work, I think. Albeit it is very surprising the first time you see it. (Doctor Hurt's line "Of course. I suppose it makes sense. 'Wearing a bit thin'!" feels more like placeholder than explanation.

It also leaves the rather odd disconnect in the story that Tennant and Smith do not realise that Doctor Hurt is from before the end of the Time War, even though we later see he dies immediately it ends. They think he could be from after it. That makes sense if he's Eccleston. Less so if it's Hurt.