My children are homeschooled but I won't try to address every single one of your points. I will, however, make a few comments. (Warning: long post below)
Our kids were in public school until the oldest (Ashley) was in 3rd grade. In 1st grade, she learned a "new math" that WA state decided to test out in select classrooms. When she got to 2nd grade, the state had decided to scrap the "new math" so she had to catch up to what her classmates were doing; most of them had learned the traditional methods and so she was effectively a year behind them.
Her teacher came in early and stayed late to help tutor my daughter; she was fully aware of the situation and worked her ass off to get my daughter caught up.
Being in the Navy, I got orders to Japan. We had heard that DoD school were some of the best available, because the DoD had the money to hire the best teachers.
Ashley's 3rd grade teacher was *not* the best. We told the teacher the situation with our daughter and explained what her previous teacher had been doing with her; though Ashley had made significant progress, she still struggled with arithmetic.
Simply put, the teacher was one of the "babysitters" you hear about so often. She didn't bother to try and help my daughter; the teacher just expected her to be where the rest of the class was. When Ashley couldn't figure out her homework, the teacher would make her stay after class to finish. However, the teacher didn't do any one-on-one with her; my daughter was expected to figure it out on her own.
One day, while waiting for Ashley to come outside, my wife noticed that she seemed to be missing. Nearly 10 minutes after all the other kids had came out, Ashley came out, crying. She said she had been forced to stay after class to finish her homework but she couldn't figure it out. My wife talked to the teacher who explained it was "standard practice" for any child who didn't complete the work in class; she also felt that Ashley was just slow/lazy but had a good grasp of the concepts.
Several days later, Ashley was again late. However, this time my wife went into the school and found her sitting at her desk, crying on her homework papers. The teacher was chilling at her desk, grading papers or some such thing. My wife exploded at her, then went straight to the principal to complain.
It turns out that DoD teachers can make $50k+ a year and have the same limitations to being fired that CA teachers have, if not more because they are federal workers. The teacher had other complaints against her but the school's hands were tied.
Two days later we pulled both our children out and have been homeschooling ever since. We annually spend more than $1200 on curriculum, supplemental books, science kits, etc. We have two computers just for the kids to use. Our children go with us wherever we go, so they get real-life experiences and knowledge constantly, e.g. grocery shopping teaches health and nutrition, addition, economic buying, change counting, etc.
Our kids probably go to more zoos, aquariums, museums, etc. than public school kids go on field trips. Being in the military, we have traveled across the US and are now in Japan for the second time.
Regarding socialization, I personally think it's overrated. When you're in school, who do you hang out with? A select clique of friends. The stoners don't hang with the motorheads, the geeks don't hang with the jocks, and so on. Forced integration, multi-culturalism, and all the other politically correct crap doesn't change the fact that people will naturally gravitate to people they feel most comfortable with.
Plus, there are ways to get socialization without being in school. Churches, YMCA, youth leagues, Boy/Girl Scouts, et al. are all available. Not to mention that the Internet opens up the whole world to finding social contacts.
My children can function in society just fine. But, for the most part, they are sick of the crap that public school children bring to the table.
They don't care about popularity, fashions, who's dating whom, or who is sleeping with whom. And they don't have to worry about being picked on for wearing glasses or because they are small for their ages (both of which happened), or deal with bullies, violence, teen sex, and all the other issues that are in the media.
They also aren't coddled with child pop-psychology, telling them that "everyone is a winner" and they are the most important people in the world. They have respect for others, aren't self-centered, and have discipline and self-control.
Their education may be different than what public school children receive but I believe they will be better able to face the world.