It is not a net benefit. It is a net loss for society, as less wealth is produced, so society in general gets poorer. It is also a net loss for those that become unintentionally unemployed. The overall salary mass is not raised, but reduced.
I would also add it is completely illegitimate to prohibit a voluntary agreement based on some supposed "greater good".
Your assertion that no minimum wage means "shitty wages for everybody" is unfounded. Wages are determined by productivity, and it's no possible to raise real wages (taking into account other goods prices) with a law. Only an increase in produced wealth can raise wages.
Edit to add: If you imply that the "unintentionally unemployed" ones are a unlucky few, that's not the case. As you would probably know, official unemployment levels are around 20% in some EU countries, while real levels are probably way above that. That means a whole lot of people is not allowed to produce nothing because of minimum wage laws. The wealth prevented from being created is huge.