Strangulation isn't painful? God I seriously hope someone strangles you to the brink of death before letting go to test your theory. You're slowly cutting off the air supply to the body to the point where it stops functioning. How the fuck is that a humane way to die or whatever you want to call it?
Properly performed strangulation results in loss of consciousness quicker than you would think. I'm not saying that the young girl in question performed it correctly, as I'm sure that a 14 year old girl would have no knowledge of how to do so, but as a general rule, I would consider any form of strangulation more humane than most alternatives. She was in a bathroom, if the options are slicing the baby's throat with her father's razor, beating his head against the bathtub, drowning him or strangling him, strangulation is in my opinion the clear choice.