I think we might be able to do without a minimum wage if we had a livable basic income. If people can afford to say no to a job, I think the negotiation balance will be much improved, and the labour market might become a lot more free.

How high a basic income would have to be for this to happen, I don't know. But I think with sufficient BI, crappy jobs will have to pay a lot more to attract people, whereas fun, interesting jobs might have more employees competing for them. That would be the sign of a healthy free market at work, I think.