Will libertarianism make us better or more virtuous? Will it restore or renew Western civilization? Try it and see. Make an experiment and see how it works out.
I'm skeptical. Some people will be virtuous anyway. Some may find that bearing all the consequences of their actions makes them more responsible and ethical. Others will remain as they are, with the virtues and vices that have been common to human beings in all ages and under all systems. Some may find out that they will be able to get away with more under libertarianism and become more vicious.
There will be those who see their opportunities and take them, and others who recognize that they will finish last in the competition, and act accordingly. Probably, as in Victorian times -- or today -- society would split into one group that is industrious and responsible and another that is unindustrious and improvident.
A libertarian order would have the same trouble with criminals and with disputes between individuals. Would the law courts be any less crowded? Would the prisons? A libertarian "society" would have a political opposition which desires to establish its own order and values, as any society does. Or would proclaiming the libertarian order set it in stone and deny the citizenry the right of changing it. In that case, new problems would also arise. If political disputes are denied other channels for the redress of grievances, revolts would arise. The dissolution of government might bring armed camps or warlords.
What is meant by libertarianism is problematic. If it's a movement to decrease the size of government when possible and effective, most Americans would probably agree with that. What's often meant is a utopian moral or religious faith that doing away with government or trimming it down to a shadow will solve long standing human problems. And this is much more doubtful.
Those who are familiar with socialism and its faith that abolishing private property will make people community-minded and virtuous, have grounds to question whether this form of libertarianism abolishing forms of all forms of coercion of the individual will make people virtuous and responsible. To the extent that we are know about life before the welfare state, we can also be skeptical.
Human beings are too varied and human nature too strong and deeply rooted to assume that such automatic transformations will occur. That's not to say that such knowledge means that we can authoritatively assert that libertarianism won't work, just that we have plenty of reason not to say that it will definitely produce the effects its supporters claim for it.