This solves the problem you get when laundering money with a food joint: you need customers.
You can launder money with a business: you pay vendors and employees with the dirty money. But then your receipts are the clean money.
That means you need real customers giving you money. So you do need to run an actual business.
(There are other ways to launder money, usually that involve spreading it around between various accounts so it becomes hard to track. But those don't require anything as elaborate as actually hiring employees, just a fake storefront so you can get a merchant account and some paperwork done.)
So a business that is cash based claims $5 million in income from sales to customers. The business pays taxes on that $5 million. That $5 million in fact came from selling illegal drugs for cash. However, to the government the money is now clean as it originates from a legitimate source. The owner of the business can then send the profit to whatever place he wants with no worry. No real customers are needed.
edit: More specifically, a drug dealer cannot just deposit $5 million in cash into Wells Fargo without police intervention, a cash based business can.
If you actually sell illegal drugs as a business, but claim to have a pizza place on your tax returns, the government might inspect you someday. If they find that you don't have any big pizza ovens, routine large orders for ingredients, staff of delivery drivers, piles of receipts from customers, etc, then they'll probably get suspicious very fast.
If you do make and deliver at least some pizzas on a appropriate scale, then things get a lot harder. They'd have to run down all of your customers and ask them if they ordered and received pizza, check if the dough order receipts are real and match the expected volume, are the delivery drivers real and how much work do they do, etc. Much more work to run down, and who has time for that? You could probably get away with it, for a while at least, as long as you didn't screw something else up.
Maybe they noticed that those adresses never cause problems (single old people) and are close enough to not be too annoying to deliver to?
Maybe they are just too lazy to do more, and it's enough for it to work?
Maybe they are using a lot more addresses but we don't get that information? But there is a limit to the addresses you can use, and you are supposed to have repeated customers.
Maybe there is something special about those adresses we don't know about?
When you launder money, you loose some of it. It can't be helped. And criminal probably don't care about not being green.
Reason to give away pizzas would be to cutdown on marketing costs, since then you’re only filter for a “customer” is people that take random free stuff.
Similar but different setup is a fake lottery, where the winner was is preselected to win and the tickets are given away free to the public who have no chance of winning but provide there information. As long as the method of controlling the winner remains secret, it would be hard after the fact to prove the “randomly” selected winner was not random; clearly people do get caught and there are ways to detect people are doing this.
One last example would be a dry cleaning service, where they offer limited amount of to good to be true offers, then stock the rest of the clothes being “laundered” via cheap used clothes purchased at second hand stores.
A lot of these patterns show up in due diligence for business acquisition, especially mom & pop lines of business.