This one will probably be the easiest to write. My thoughts & feelings are pretty well set.
This method works for some. If you are using it because it works, great. However, if you are using it because you truly feel that it is the only way to get a proper education or because you don't understand your many options, I suggest doing some research (with an open mind).
Now, let me first lay out what I mean when I say School-at-Home. Then, I'll explain what I do and don't like about it. This is what I envision when I think of School-at-Home:
Typical scope & sequence of the public school, even if accelerated or slowed down to accommodate the student
Use of textbooks (especially the same one public schools use) and/or workbooks for most or all subjects
Set amount of time for each subject, often with very short or no breaks between
Most of day spent at desk or dining room table
Mom (or dad) has teacher edition/answer key and 'teaches' the lessons while the child sits & listens, possibly taking notes, all discussion (if allowed at all) held to end of lesson
Most or all assignments are graded
Tests are common in most or all subjects
Lesson plans and not allowing student to stray from plans are common
Book reports, recess, and homework are words I would only expect from school-at-home style homeschoolers
Concern about 'keeping up' with public school peers is common.
As you can tell, I see School-at-Home very much like school, but at home. Now that we know what I mean when I say School-at-Home, let me say what I think about it.
*I think it's too rigid. I think that most students would benefit from at least some deviation from this. I know it works for some, but it's not a method I would use.
On a personal note:
The way public schools do things didn't work for me (and that's also counting the Gifted program which used more hands-on work & involved a bit more critical thinking & creative work). It wouldn't work for my kids, either.
It is way too rigid for us. Yes, we need some routine, schedule, and stability. However, we also need some freedom & flexibility.
I am not a fan of textbooks for most subjects, especially in the elementary years.
My kids would be bored out of their minds and would rebel if we used workbooks & textbooks for most/all subjects.
I don't feel that textbooks and workbooks offer the opportunities to use higher forms of thinking & learning.
My kids are not 'average' or 'typical.' Therefore, they don't progress at the same rate as their same age peers. Plus, I prefer a different scope & sequence than that used in public schools. So, the public school scope & sequence, expectations, and rate of progression simply would not work for us.
Most importantly, I want better for my kids than the public school can offer. Therefore, using their methods, materials, scope & sequence, expectations, and one-size-fits-all mentality doesn't make a lot of sense to me.
Now, as I said, if this method works for you, use it. However, if your only reason for using this method is lack of understanding of the options or because it's what seems most familiar, look into other ways of educating.