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I have found it is roughly an order of magnitude cheaper to cook at home, even once you factor in the "lost" time.

The amount of time required to prepare incrementally larger batches increases at a sub-linear rate. The bigger your batch, the more food you get per unit of wall clock time. I try to prepare no less than 3 lbs of dry beans or 2 lbs of beef at a time. Anything less does actually feel like I'm wasting my energy.

I can make about 2000 calories for about $2-5 using staples like rice, beans, flour, salt, yeast, pepper, etc... Generally, spices are pretty cheap. Especially if you go to the bulk section instead of buying the little jars.

The thing I see stopping most people in poverty is lack of access to a kitchen. No oven, no stove, no pantry, etc... A hot plate and a microwave if they are lucky. Also the usual health issues that come from deep poverty like executive dysfunction, depression, and other chronic illnesses.

>roughly an order of magnitude cheaper to cook at home

Why should this be the case in principle though? Do economies of scale not apply to food preparation?

Yes, but then you have to account for tax, pay, shipping, wastage, theft, and (most importantly) rent on both kitchen and storefront.

The homeowner does not charge themselves rent for their own kitchen, nor for their time.

They do and companies already take advantage of them. But even a fast food restaurant has a ton of additional overhead that you won't have by cooking at home (or some you won't include in your price of your homecooked meal): rent, salaries, utilities, taxes, shrinkage, maintenance, etc. So even if they can get the ingredients cheaper they can't compete with you on some of these factors and must also include others like utilities in the cost of the finished product where you will generally ignore them when thinking about how much it costs to cook dinner.
In a lot of cases it's simple price fixing. If you want to be shocked, compare the prices of frozen potato products (like bagged hash browns and french fries) to the price of potatoes. There's like a 200% premium for simply cutting and flash freezing them. The machines have got to pay for themselves in an hour.

Does it make economic sense? Yes, when you know that there is a frozen potato cartel: https://www.potatopro.com/news/2024/alleged-potato-cartel-ac...

If you want to make your own frozen potato product like this you also need to parboil them. Otherwise the results are acceptable but underwhelming.
Once you factor in rent, then cooking at home is maybe not cheaper. Rent and mortgages is the black hole sucking all money from the restaurants. Not ingredients or wages.
On the other hand, how high is the marginal rent of a kitchen at home? It's usually included whether you use it or not - and some parts like the fridge would take up space even if you exclusively ate out.