If we believe that suffering is valuable for the excellence of humanity (not just for individual human beings), it seems to justify a political system that actively neglects the welfare of its citizens. To say nothing of the intellectual dishonesty of claims that suffering builds character when said from the vantage point of those who can choose not to suffer.
In the end, I actually think Nietzsche's political philosophy is wholly compatible with something resembling the modern welfare state: insofar as we can understand suffering to be valuable, it is only so when it is an active, human choice. Those forced into such a position may find themselves closer to "the whole damn truth", but only incidentally. And human experience is rooted in the choosing. The power of Martin Luther's oft-(mis)attributed "Here I stand, I can do no other" is not in its truth -- he obviously could have done otherwise, but he chose not to. Without the capacity to make those decisions for ourselves, to be allowed to decide that truth is worth the loss of happiness, achievement, fulfillment, we are never ourselves truly human. That some (many? most?) may decide the 'easier' path of herd morality doesn't change this: we are, by virtue of our humanity, able to elect not to be human. That so many do is a tragedy, yes, but an understandable one; and the possibility and fact of this tragedy gives meaning to the choice itself.