If the labor market caused employees to be paid more, would the employer refuse? Shut down?
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.
Businesses are profit-maximizing organizations. They operate at maximum profit, not at the lowest! A business's managers don't meet to consider the lowest profit but how to maximize it. Critically, they don't price what they sell at (costs + some profit); the price it for maximum profit regardless of costs.
Some businesses have enormous profit margins, some businesses sell at a loss - many businesses do that regularly (e.g., clearance sales) - because that is the best they can do. Some sell at a loss strategically to gain market share, a common tactic of well-funded Silicon Valley companies.
> 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.
From the business owner's perspective, wages are a cost. Costs, including wages, go up and down all the time. If you make TVs, the price of glass might be X one month and 1.5X the next.
The business brings in revenue, which it splits between costs, investment, and profit. When costs increase, you can raise prices (which reduces demand, as you say, and also drives away customers longer term) or reduce investment and/or profit.
Also, the relationship between price and demand isn't linear; it varies by price and by good/service: Increasing gas prices temporarily may not impact demand much because most people have little choice but to drive, though in the long term they might make adjustments. Increasing candy prices, on the other hand, could have a big impact because most people can easily eat something else.
The employer of the person in the OP has a choice if wage costs increase: Increase prices, reduce investment, or, heaven forbid, reduce profit (reduce their own income).
If the profit in this business becomes less appealing relative to other businesses, the owner will change businesses, there will be less competition in this business and the prices will go up. Increasing potential profit.
This is basic stuff. Despite your aversion to business owners making a profit and wishing employees were paid more, introducing non-linearities, loss leaders, price inelasticities or any other complication does nothing to change the fundamental point.