You seem to be perpetuating the idea that class size determines educational quality, and it ain't true. Indeed, it seems that many people take class size as a proxy for the quality. But it's false.

If you go looking for actual data on the relationship between size and educational achievement, you'll find that it's pretty inconclusive. Nobody has been able to show a strong correlation linking smaller classes with better learning. The one exception is a study showing that in the specific population of "at-risk kids" (meaning, those who are probably not getting educational support at home), having smaller classes does help. But for the mainstream, nobody has been able to prove that investing in more teachers to shrink the size of classes has any positive impact.

Continuing to harp on class size is part of the problem. It wastes money, preventing it from being employed in areas where it could do real good.

That's not a class size or teacher problem, that's a furniture problem.

and their preparation time has been eliminated

I call BS. Does somebody come home with them and prevent them from preparing. As a manager and software developer, I spend a fair amount of my own time researching a prepping. Why should teachers not do the same?

7 classes per term, average of 40 students per class = 280 students total. There are 7 classes per day of 45 minutes each, with 5 minutes between classes and a 30 minute lunch. Teachers have to meet with students before and/or after school and monitor students between classes, so they're typically at school and busy for 8 hours or more per day with no breaks except maybe lunch. You try locking yourself in a building with 1000 or more shouting young teenagers for 8 hours straight without so much as a bathroom break.

If a teacher assigns a homework assignment every day and spends three hours per day (at home) grading assignments, then each student gets less than one minute of attention per assignment. Every student has his or her own points of confusion on the subject matter, which cannot be addressed in just one minute per day, and using class time to broadly address the questions of a few students slows down the students who don't have the same questions.

Notice I didn't include any time for designing lesson plans and presentations, writing grant proposals, creating assignments, or meeting with parents, let alone spending time with their families (which often enough just doesn't happen).

Regarding "furniture problems:" desks are a fixed size, they have to be spaced apart enough for students and teachers to reach them without tripping, and the classroom also needs presentation space at the front, a teacher's desk, and storage space. Fire codes specify maximum occupancy limits for rooms. There's only so much room available for desks.

Maybe you have to see the combined exasperation and exhaustion of an overworked and underpaid teacher to appreciate the level of decay present in our public school systems. This is an area where averages and statistics are misleading.