"Consent" is tricky in this situation, because for many, it's do this or starve.
While it's certainly true that if these jobs were forced to pay a reasonable minimum wage there would be some less work to do, most of the world has already conceded the point that pure supply-and-demand is not an acceptable way to negotiate wages - we agree that some minimum wage is useful to protect those without other options.
If I weren't already off-topic, this is where I would veer into advocating for basic income.
I would love to see the data, but in my experience of growing up in a very poor neighborhood, getting a foot in the labour market is the difficult part; once you are in, moving up is relatively easier.
I'm not saying the minimum wage or automation are bad, but it's simplistic to claim wage levels and employment have no relationship.
So if we agree that at some level of the minimum wage, businesses would not be hiring someone because they cannot pay them below minimum wage - then why do you think this is not happening to some people at the current level of minimum wage?