>If they tended to seek employment elsewhere, which I believe to be the case, then that makes my point.
That is ignoring the point you actively quoted. Once wages decrease enough workers exit the workforce. There is no reason for them to continue working when the costs of living outstrip their wages. This is not even a hypothetical, you can look at modern families that decide to have a parent stay at home because daycare costs outstrip their salary to see this in effect today. You can imagine this happening of wages got so low that a person would be able to spend time growing their own food and getting more free time than if they worked and traded their paltry wages for food.
Having all competitors increased wages would have pulled more workers into the workforce from the pool of people who had decided that they got better value out of doing their own thing rather than working for a company, so everyone would win.
>This doesn't make sense to me. If employers didn't have enough staff, they would increase bottom wages in order to fill those positions rather than forgo potential profit and business health. If there is unemployment and bottom wages are low, then that says something about the labor market, not minimum wage
You are mixing two concepts here. You see correct that if unemployment is high and bittom wages are low then the market is not valuing that labor. The government is mandating a minimum wage would still bring more workers out of the "not looking for work" section of society into the workforce by increasing the benefit of working for those workers.
I feel as though you are suggesting that companies should only pay what workers are worth to them and the government should stay completely out of it. That is a logically consistent viewpoint if you are ok with people who don't currently have a valuable skill dieing in the streets from poverty. Our society,in most western European derived societies, has decided that this is not acceptable and has put in social safety nets to prevent this.
When an employer pays too little to live and the government has to step in to provide enough extra for the employees, that means every taxpayer, including you and me, are now subsidising that employer. If the government wasn't there then the workforce for the employer would either leave them or die off and the employer would naturally be forced to increase wages or go out of business.
As it stands I see three options for society, and only 2 ethical ones.
Option 1, the government taxes everyone enough to provide ubi and employers no longer have any limitation on them concerning minimum wage or other compensation. If they want to offer 1 penny per century and someone agrees, that's fine.
Option 2, minimum compensation is encoded into law and increased to the point where the government no longer has to provide any welfare
Option 3, which I personally find immoral but would be logically consistent, is that we go completely laissez faire so employers can offer what they want, the government doesn't tke taxes to provide welfare, and of a citizen doesn't have a valuable skill they either learn a valuable skill or die from lack of medicine or food