And since you haven't shown any data, your anecdote is skewed by including Switzerland and the US in the same category. Despite no national minimum wage, about half of Swiss workers are covered by collective bargaining, which does include minimum wages (and presumably, as is true in the US, helps raise wages of non-bargained labor). And the other developed countries with no minimum wages (the Nordics) have even more of the workforce covered under unions/collective bargaining. Which again- does include minimum wages, but done by sector instead of for the whole country.
Also, see here for graphs of developed countries.