Karl --- Sure, I agree that in an infinite-horizon formulation you can always find a discount rate that justifies any amount of present human suffering. This will be especially true if your discount rate is greater than 1 (e.g. next year's utility is valued at 1.1 times the current year's).
But this doesn't necessarily argue that our models should have a finite horizon - it's equally reasonable to say that our horizon should be infinite but we should choose our discount rate with care.
For example: why is a finite horizon model for human achievement/happiness/economy preferable to an infinite-horizon model with a steep discount (say, 50% per year - next year's utility valued at half of this year, two years from now valued at 1/4 of this year, etc.)? The series of coefficients does converge.
The reason I ask this is that I agree that everything will eventually end badly, whether that's due to climate change/nuclear war in five years, or the heat death of the universe in tens of billions of years. But it seems to me that there is some tiny slim chance that our species will survive for a long time and maybe even spread beyond our planet, and I would like for the possibility of a good outcome like that to influence our decisions.