Thanks! I must respond a paragraph at a time.
From a simple supply and demand standpoint, we still have fewer jobs than workers looking for hire.
I disagree: you ignore price, one axis of a supply or demand chart.
From a worker's perspective, income opportunities exhibit scarcity: you can't just collect as much income as you want while sitting around. And you only have so much time and energy you can offer to employers.
From an employer's perspective, employees exhibit scarcity: you can't just employ as much labor as you want to use; you are limited by your salary budget.
The supply and demand curves should intersect at a market equilibrium which establishes the price, just as they do for coffee or gasoline.
(Aside: I often see the idea expressed that one party can set prices, such as greedy airlines charging baggage fees, or airport bars setting high prices for drinks. People can ask any price they like, but the market price is determined by completed sales, which require agreement from both sides.)
I think of a job as a person selling their time, energy and talent. The employer is a customer of the worker. There are differences between being a customer of an airline, of a coffee shop, of a cell phone carrier, of a piano tutor, and of an engineer, but not differences that I see changing the economic fundamentals.
If prices (in the job market: wages) go down, there will be increased demand from employers, meaning a greater number of paid hours worked: more jobs. If prices (wages) go up, there will be reduced demand for labor, meaning fewer paid hours, and more demand for labor substitutes, like automation. This is the adverse outcome of higher minimum wage. [Edit: on reflection, this paragraph is sloppy. A change in price is the result of a change in demand, supply, or both. Lower prices could reflect greater supply (leading to greater volume) or reduced demand (and reduced volume).]
This, in tandem with the federally-mandated minimum wage offered to labor by a large number of huge corporations, effectively cripples any competition in the unskilled labor market.
I agree that minimum wage distorts the labor market. It creates a surplus of workers who cannot sell their labor because it is overpriced. Workers cannot "compete on price" so there is always a line at the door.
It may be unpleasant to imagine sellers of labor competing in a "salary war" though we love nothing more than a price war among sellers of mattresses or laptops. But it is far from obvious to me that one worker getting a high salary is better than two workers splitting that same salary.