Once you make this job illegal, what do you think she does then for a job? By taking this job she has revealed that this is her best option. When you make the job illegal, you're forcing her to take a worse alternative.
What is that based on? The employer is making a profit; they can reduce those profits and pay employees more. It happens all the time in response to the labor market.
If the labor market caused employees to be paid more, would the employer refuse? Shut down?
It is based on the idea that the employer is running a business and competing with other businesses to provide the best product at the lowest cost. The employer is operating at the lowest profit he considers acceptable. In your imagination there is some "labor market" which is going to coordinate to bring all these businesses to an impasse. That's not going to happen.
If somehow the labor market was able to coordinate to demand higher wages, the business would have to increase its price. There would be less demand at the higher price. Consequently there would be fewer businesses and fewer workers would have jobs at all.
