Well, what I presented was anecdotal... I didn't know there was formal research to back up my opinion.
However,.... this doesn't mean that pedagogy isn't a skill.
Sure it's a skill. However, it's a skill that the educational system thinks it is rocket science, when it is something easily figured out through OJT by many, if not most, parents. Most parents have a pretty good idea about the level their child is at, and can figure out pretty decent ways to communicate concepts to the child, whether or not they have had formal training in it.
SImilarly, none of #1, #2, and #3 are interchangeable. And I'm sorry, but "corporate training" isn't interchangeable with "elementary school education," either
Interchangeable, no. However, you learn a lot doing corporate training that does DIRECTLY apply to teaching children. If you don't believe that, try doing a corporate training session without providing donuts / coffee / snack!!! Seriously! You'll see tantrums that rival the worst 6-year-olds!
-- that's why educational psychology and adolescent psychology are on the list of courses for the education certificate I listed above. Children are not just short adults; their cognitive and social development is quite different. The material and presentation appropriate to teaching an eight year old is often radically different from the material and presentation appropriate to teaching the exact same subject to a fourteen year old, and different again for a thirty-year old. If you don't believe me, look into the literature about the various stages of language acquisition, and about "age-appropriate" language teaching. My college French textbook would be terrible for teaching six year olds who don't understand the distinction between "nouns" and "verbs" in their native language, but six year olds will respond like sponges to an immersion-style approach.
Well, duh!
A teacher needs to learn to present material in an age-appropriate fashion. And if you think the experience of corporate training has no value in learning that skill, you obviously have no idea what it's like to do corporate training.

Try teaching an executive level person about computers! GAH!!! I'd rather teach statistics to fourth graders!!!
Naturally, any schooling approach has pitfalls. The problem with homeschooling is that the people doing the schooling are often -- as this thread has amply illustrated -- almost entirely unaware of them. The problem isn't that good, skilled, well-educated, self-knowledgeable parents will homeschool badly. The problem is that well-intentioned but clueless parents do not recognize that they do not fall into the group above. There's some citation floating around on this forum that I don't have to hand about how hard it is for below-average students
even to recognize that they are below average. This weakness isn't restricted just to students; it applies to
everyone.
This is true. However -- even those parents who are below average generally do not homeschool in a vacuum. The vast majority of homeschoolers work with published curricula and/or homeschooling networks / support groups. There is help available, and -- if we can assume, and I think it is fair to do so, that most homeschoolers are well-intentioned -- even if a parent cannot recognize himself as below average, he probably can recognize when another in his group is
better, and will avail himself of that resource.
I know I'm an effective teacher. I self-assess myself as doing quite well.
More importantly, I know I'm an effective teacher because I undergo a regular "peer review" by my fellow faculty, and because I had a extremely stringent evaluation a few years ago when I applied or promotion and tenure, and they did everything but a blood test. Public school teachers don't have exactly the same system, but they have something close, often including an official mentoring system and a state-mandated process of continuing education to make sure their skills are up-to-date. (Heck, even college faculty don't have the continuing education mandate; I could have gotten my degree in 1967 and never opened a book again in my life. I used to teach with a few of them, but we don't tenure that type any more precisely because they aren't very good teacher.)
Up-to-date skills do not make a person an effective teacher. Frankly, if the evaluation system worked as well as you imply, then there would be no ineffective teachers in the public schools, and that is far from the truth. Particularly in bad neighborhoods, some school systems are begging for teachers, and the systems wouldn't consider cutting a teacher no matter how ineffective.
In really nice areas, such as my own Howard County, MD, teachers are begging for the opportunity to teach here, as opposed to going into, say, Baltimore City. The HoCo school system has much more opportunity to pick and choose teachers based on effectiveness, skills, and proper evaluation methods. Unfortunately, that isn't the way it is everywhere.
Tell me again about the evaluation process for homeschooling parents?
Well, it is mostly self-evaluation, and that can be problematic. On the other hand, it is easier to evaluate the students. Where I'm familiar with it, homeschoolers have to present a portfolio of work to a representative from the public school district to show that their child is making progress. If there is a problem with the child's progress, it (hopefully) becomes apparent. Then, presuming again that the parent is well-intentioned, they would reassess the situation -- not necessarily to find themselves below average as a teacher (the blind spot you mentioned), but at least to explore possibly better alternatives.
In any case, homeschooling isn't for everyone, but I think it is far far far less a problem than many people think it is. And I also think the educational system and many professional educators feel, unfortunately, threatened by homeschool successes, rather than happy for those kids.