Equally, if employee Y is producing the same quality of work as employee X but trying to charge more money, does employee Y not deserve to be out-competed by employee X?
Employment is a two-sided market too.
Nobody would advocate for a minimum price for a packet of crisps just to save the poor crisp companies from earning too little per packet. It is obvious that if crisps were too expensive, people would stop buying them. The same applies for workers.
Minimum wage is just saying "if you can't produce at least $X of value per hour, you're not allowed to work at all". That's not fair.
Non sequitur.
Also, inaccurate. You can't _legally_ work if you can't produce $X of value per hour. Of course you can work; it'd just be illegal. The oldest profession in world is, after all, prostitution. And there's demand for that.
Also, if you can find applicable work or not is not entirely up to the potential worker. That's supply AND demand.
Which means you end up working illegally (in a what I'd argue is an uncivilized society) or you end up with social benefits (in a what I'd argue is a civilized society).
Which means, following your logic: "if you cannot be profitable while paying your employees minimum wage a $X/hour, don't have that job available."
In other words, if you cannot pay your workers a fair fee while delivering food, don't deliver food at all. But I guarantee you its profitable. Food has been delivered for many decennia. I remember as a child in the '80s we had a minimum order fee, a delivery fee, and a radius where orders were delivered to. Some companies still do that.
Of course, we end up competing with migrant workers from less free areas in the world. But that does not mean we need to lower our standards to those of where those people come from.
As a final note, its important that minimum wage laws exist because they're roughly the minimum means to an end in society. The minimum required to have food, a roof, insurance, and basics like an Internet connection.