I don't know where you've been finding this argument but it's hardly representative of a good argument for libertarianism. I grew up in Europe (well, the UK, which is kind of Europe) with Labour voting parents and grandparents with fairly socialist views and considered myself a socialist into my early 20s. Weak arguments like these wouldn't have been enough to convert me to a generally libertarian worldview.

I had a similar caricature of the views of supporters of the free market (back when I didn't even know the term libertarian) but learning more about economics and being confronted with evidence of better outcomes in freer economies, together with learning that few serious economists (or libertarians) believe in perfectly efficient markets and learning about Public Choice Theory were key in changing my political views.

Key to the economic arguments for libertarianism is the idea that incentives matter and that the incentives facing actors in a free market tend to be far less perverse than those facing politicians or employees of state run monopolies.

The moral arguments stem largely from a view that personal freedom is a high moral value and that the evidentiary bar should be set very high for any demonstration of harm to justify restriction of individual freedoms. That tendency seems to be correlated with certain personality types according to some research and the crossover between libertarians and progressives/liberals on social issues seems to be as much a factor of personal values as of consequentialist reasoning.

And being fairly familiar with UK politics (less so with European politics in other countries) the idea that European politics pick policies based on 'what is estimated to work best' strikes me as pretty laughable.