That was prevented only because of strong unions effectively setting a minimum wage for their industries. Hence why non union workers where getting shafted.
Especially the Ruhrgebiet has quite some stories of that regard. It shines an interesting light on the history of the german social democrats and their relationship to the communist party, given both their interest in the approval of the workers, and is a - mildly put - embarrassing comparison to the state of the modern SPD and its political vision (its Gestaltungswille).
Might be a bit OT for non-germans, but most countries - apart from the USA, afaik - should have a similar part of their history.
Countries like Denmark and Austria are sometimes touted as examples of how you can have no minimum wage and still good working conditions, but they really do have something very close to a minimum wage. It's negotiated through a corporatist labor framework rather than passed directly by a legislature, but the end result is that 98% of Austrian workers and about 85% of Danish workers are covered by a minimum wage (in Denmark it is 109 DKK, about €15/hr).
Germany by contrast has much lower rates of union coverage (69% as of 2003, and rapidly dropping), making that mechanism less effective. One solution could be to introduce a de jure minimum wage, as Germany now seems likely to do. Another solution could be to change Germany's labor framework so it's closer to the one that prevails in Denmark and Austria, countries that have systems that more or less guarantee that large workplaces are always unionized.