Yeah, I've heard stories of teachers having way over the contractual max for students, and I witnessed it myself in high school. I've heard stories of kids having to sit on the floor because there were too many kids and not enough desks, and the admin didn't want to pay for more desks...and computer classes with not enough computers, so kids have to take turns.
I definitely agree that it's a different set of circumstances between a classroom and a household. I just parallel them in my mind because they are about the same amount of kids, and I'm an only child, so I didn't grow up with a house full of siblings. I find it so ridiculous that they expect 1-2 adults at a time to keep an eye on that many children at home, especially when they have been known to have unsecured firearms, steep stairs, possible chemicals, etc.
In a classroom, it is easier to handle a large number of kids than in a home.
The entire classroom is designed for kids of a similar age, unlike a home which has many ages. The classroom can be prepared by an adult in advance. Meals come mostly ready for consumption in bags, or are made by others than teaching staff. There is janitorial staff, and administrative offices- and hopefully a nurse. If someone arrives to visit the school, someone other than teaching staff greets them.
A home is used 24/7 for many purposes, and it is not usually cordoned off, the kids that live there have beds upstairs, the family room is for all ages and adults, too, and can not only have age appropriate items. Children can be expected to stay in certain locations at certain times, but that is harder to enforce in a home, where the rules could change more rapidly when there are more or fewer kids or teens, or new babies appearing like magic.
A home bathroom could be packed with hazards. There might be a potty for a two year old and a regular toilet that a 1 year old can drown in, but the 4 year old cant get around a safety lock and waits until the last moment to run to the bathroom, so it is not used. The 8 year old leaves their legos out, which the babies that have become mobile want to taste. Opening up the bathroom upstairs causes total loss of control of the group, plus adds the hazard of the stairs. The 13 year old forgets they’re heating up the curling iron, and the 17 year old leaves a hair dryer plugged in when the baby they are assigned to starts crying. and a 10 year old, climbing onto the vanity to experiment with borrowed make up, kicks the dryer into the toilet. Anything that causes the toilet to clog, such as a jealous sibling flushing away someone’s favorite toy, becomes an emergency because the upstairs bathroom is available but causes a great un-corralling of the charges.
Unlike a teacher, the parent figure has to deal with preparing and serving food, cleaning up slippery or germy messes, plumbing problems, the doorbell... and a multiage group. Unlike a teacher, ill children could be present and expected to stay and be cared for sick.
The hazards connected to food prep are many. The hazards related to cleaning products used in a rush are many. A 6 year old threw up in the hall, and the English muffin pizzas the kids prepared themselves are under the broiler and are about to burn. A quick clean up, and perhaps the cleaning product is left out, the pizzas are served, but the six year old has to be checked for a fever, hopefully nobody feeds the babies anything they will choke on while the 6 year old is put to rest on the couch, with a pot to vomit in. Hopefully, a well meaning 8 year old does not take the cleaning product to the babies’ sticky trays while the babies are still in them. And hopefully nobody releases the babies while an adult is trying to make sure the 6 year old is ok.
There are ways to make this safer, such as having a baby area where only baby toys are allowed, but this requires setup, which is tough in a home, once again used 24/7. The best way would be with a station system, rules for is allowed to join each station, and dividing sister moms and brother dads to be responsible for various stations, I think. But the home is going to look like a huge classroom and a maze of baby gates. It wouldn’t look like a home.
As a teacher knows, planning is a proactive way to prevent problems, but it is much harder with so many different ages. I think the homeschool curriculum pretty much is designed to teach all ages (or not teach all ages IMO) and there are some things you could get many ages engaged in, like some food prep, some art projects, some gross motor activities such as a follow the leader game where oldest kids carry babies, but there is a huge difference in what can keep babies, toddlers, 4-6 year olds, etc. engaged and out of trouble. All day long. No cafeteria period. No separate gym teacher. No clean up crew after the food prep or art projects.
So, even with full organizational and child management training, and an organized physical area where the children are expected to stay, perhaps divided into stations, the number of children that can realistically be supervised in a home is fewer than the number in a classroom, IMO.