Socialism itself doesn't prevent you from hiring someone for $4 an hour. Current laws (which may be based on socialist principles) do that. You could argue that, in a future with a universal basic income, we wouldn't need a minimum wage, as people could survive on even no wage. Would this be more or less socialist than things as they are today?
>Does the absence of a modern state which meets this criteria prove the point? Hardly. It does not follow.
Prove beyond a shadow of a doubt? Of course not. Prove within reasonable heuristics? Depends on your definition of "reasonable". Our definitions are clearly different.
>Take any sector of the modern economy which is heavily affected by socialist programs and you will find a sector which is scraping by.
A failing but necessary industry is one ripe for being regulated by a socialist government. Perhaps it is not the socialist regulation that caused the failure, but the failure of the industry to meet public need which drives regulation. You may find this reversal (or un-reversal) of cause and effect ironic, but it really comes down to the classic correlation vs causation question. Without better research, we really cannot know.
For now, I am comfortable with the concept of a government advocating on my behalf for the purposes of improving aggregate outcomes. Certainly, governments may fail or do poorly, but I do not think it is a pointless effort. It sounds like you disagree.