So he begins by acknowledging that many of the minimum wage workers would be fired. (Keep in mind that's one of derleth's bullet points he called Yglesias a 'moron' for.)

No, he's a moron for assuming it will happen one minute and then forgetting he's assumed it the next. He presumes that teenagers will be able to take part-time jobs at restaurants, forgetting he's assumed that those very jobs will be automated away!

Or in other words, as I read this, some employees would be fired, and some would be promoted, with automation taking over for the lower skilled employees who were fired.

I cannot see one single reason to assume there would be "managers" as such at these automated restaurants. Do you assume the machinery would need constant tending and monitoring? Because that would be a rather big flaw, which the machine-makers would design out.

Freeing up labor by creating a new industry seems like a classic Kaldor-Hicks improvement. I share derleth's skepticism about transfers being made, but I don't think someone is a 'moron' for suggesting it.

He's a moron for suggesting that a recently-fired worker would care one damned bit that someone else got a job.

We have a need both a) for more labor in these sectors, and b) a need for better training and screening. These are not mutually exclusive, or zero-sum. And arguing for things that would reallocate labor to them doesn't imply you want to kill kids unless you're a fucking psychopath.

'Reallocating labor' to childcare is not that simple, and if you think it is, you want untrained people caring for children, which means you want to kill kids. There. Simple enough?

1. It requires training. This isn't free. It isn't even cheap, if it's any good.
2. It requires screening. This begins at a criminal record check. It doesn't end there if you don't want to kill kids.
3. It requires a cultural fit. That is, it requires that people be good with kids, and be psychologically fit to take care of them. This is, I suppose, part of screening, but it really deserves its own point.

So, which of those things do you want to skimp on to shunt all of the fast-food workers into childcare positions?

I think Yglesias thinks that when we make things cheaper, and lower the cost of living, it increases the amount of leisure workers are capable of taking advantage of.

Why would automation necessarily make anything cheaper or lower the cost of living? Are you assuming a progressive taxation scheme, or the absence of collusion in the business world, or both?