> Either that job is an internship (non-permanent and I already addressed it) or you will quickly become a fully productive worker (this is literally just training/ramp up and is not a significant cost to employers).

You're asking for examples and then pigeonholing any possibilities into one box or the other.

Some occupations take a long time to learn. Years. Particularly if it's effectively half training and half working, because then it takes twice as long to finish the training. If it's the equivalent of four years of undergrad and three years of grad school then it would take fourteen years -- hardly "temporary" but at the end you would be qualified for a six figure job and have no student loans. Is that a sufficient example?

> Companies can and do regularly lobby for laws. They don't appear to be using this line of reasoning because if large minimum wage employers like McDonalds or Walmart tried this they would be laughed at even in political spheres.

The institutions that would lobby for this legitimately don't exist because their structure is prohibited by existing law, so it's chicken and egg.

Existing large minimum wage employers generally don't want to eliminate the minimum wage because it would make it harder for them to retain talent because their prospective employees would have more options.

Suppose you work at McDonalds and have a 30 mile commute. That costs you thousands of dollars a year -- you have to buy, maintain, insure and fuel a vehicle -- and about eight hours a week of sitting in traffic. A job that paid $2/hour less but was close enough for you to walk to work would leave you healthier with more money in your pocket and more free time. McDonalds would have to pay you more in order to get you to not quit and take the other job. Why would they want that?

> People take badly paying jobs because if you're faced with bad and really bad, you'll take bad. Companies are free to exploit this without minimum wage laws in place. This type of exploitation only works in a buyers (if we put employees here as "buyers" of jobs) market, and immediately pushes wages significantly lower in a sellers market, which we have seen for quite a good deal of the past few decades. We can't have economics that are only moral when things are going well.

But that's the whole problem, isn't it? When things are going well it's a seller's market and you don't need a minimum wage. When things are going poorly, the option isn't minimum wage job vs. less than minimum wage job, it's less than minimum wage job vs. unemployment. So then you're prohibiting bad and leaving them with really bad.

> You are improving the lives of every job that has a raised salary as a result.

You're also worsening the lives of every customer who has to pay more for goods and services as a result, and for that matter everyone who makes less on their retirement account. That part of it is a zero sum game. The part that isn't is the part where where the minimum wage prohibits Pareto-optimal alternatives that generate actual surplus.

> Big citation needed here.

If there exist two complex options and you take one away based on a simple factor, there will be some number of people for which the option you took away was the better one. Can you not imagine that some jobs might pay less money but be more flexible or closer to home or less emotionally taxing and thereby preferable despite the lower pay?

> There are many studies on both sides of the minimum wage debate, and that's just going to turn into a linking war between people who are not economists and are also not likely to change their minds on the internet.

All of the studies of this question are inherently politically compromised because it's trivial to design a study to find the outcome you want. If you want to see no increase in unemployment from a minimum wage increase, find one where hardly anyone was making the minimum wage even after the increase to minimize the economic effect. If you want to see a large effect, find a large minimum wage increase in a place with many small businesses that can't absorb the higher costs and few large institutions that can.

The ability to cherry pick data doesn't prove anything. But notice this: Even when a minimum wage does exactly what you want it to, the effect is to transfer money from the large institutions that can absorb the minimum wage increase to the minimum wage workers. But you can get exactly the same desired effect simply by changing their relative tax rates (using negative rates if necessary) without incurring any of the harm caused by constraining anyone's choice of employment.