I don't think a minimum wage is ethically justified in a minimum standard of living society
unless that value in progress through automation is justified.
The arguments for minimum wage are always to insure it provides a livable wage, but economists generally rightly dislike it for limiting labor opportunities to ones above that wage threshold.
In the absence of a minimum standard of living you rightly should cling to minimum wage laws like the lifeboats they are for the working poor. Once participation is voluntary forfeiting minimum wages seems like a very promising bargaining chip against capital to get a negative income tax / UBI actually put into law.
I think I'd rather see UBI / NIT and have progress towards the singularity slowed for lack of a high minimum wage to pressure automation than the status quo of extreme unhappiness and poverty (and the corresponding social unrest, drug abuse, crime, mental illness, physical ailment, etc). Of course if we can have our cake and eat it too that would be great... I'm just saying to leave the minimum wage on the bargaining table, insuring survival seems like the more important goal.