I’m pretty sure slavery is outlawed in all European countries so that alone prevents a 0 minimum wage. That itself is a regulation. There are lots of “regulations” (government interventions) that prevent a zero minimum wage. Indeed the legal protections and regulations regarding unions, social programs for the unemployed, universal healthcare, etc. all contribute to an environment where the lowest wage isn’t zero. It is not a stretch at all to say that the legal infrastructure surrounding unions and requirements surrounding dealing with them count as “regulation”.

There are lots of instances where regulations fixed a broken system. Government regulations fixed the broke system of using child labor and fixed the broken system of slavery.