Anecdotal experience chiming in here...
I am the middle of 5 children, and all 5 of us were educated at home by our parents. In response to your claims, I will use the 5 of us as examples.
1.) My older brother (who is the oldest) graduated from home school and then proceeded to community college. He received his Associates, but he decided that he did not want to further his academic career. He is 31 now and he works in the professional services side of a major patent law firm. He makes close to $100k a year, is married, and has two boys. He is also actively involved in the local music scene in his city.
My older sister (2nd oldest, 29) graduated from college with a communications degree. She now works for a major U.S. professional sports team in the marketing/analytics side. She is not married, but she makes close to $100k a year and travels across the U.S. and world constantly. She also studied at Oxford on scholarship for a year while in undergrad.
I am the middle child (27). I graduated with my undergrad degree in government and international politics. I currently work in the private sector side of government affairs, but I have also worked in the US. House of Representatives. I don't make quiet as much as my older siblings, but I am advancing in my career quiet well and content with my career path. I am married, have 1 kid and a home. I also coach youth football and soccer.
My younger sister (23) is currently in graduate school pursuing her advanced degree in athletic training. She is on full ride scholarship and will most likely go for her PhD. She also studied at Oxford.
Youngest sister (20) is currently in undergrad and moving along quite well. She has also studied at Oxford on scholarship.
2.) This can be true for some home school children, but that was not my experience. My parents were heavily plugged in to different home school groups in our area and pulled resources for different subjects. This is usually done in the form of "home school co-ops"
I was taught chemistry by an individual with a graduate level degree in chemistry, and math by an individual with a graduate level math degree.
There are also many, many online schools and learning resources for home school students. A lot of home school students will also duel enroll with their local community and start receiving college credit in-lieu of AP courses.
It all depends on how much the parents want to reach out to their local home school community.
3.) Again, this is all my anecdotal experience, but I feel very connected to my community and job. I would say my siblings do as well. We have friends, spouses, hobbies, and are well adjusted individuals.
Contrary to a lot of "Hollywood" depictions, we were not locked up in our home all day shut out from the world. We played sports, we were involved with local theater groups, etc.
4.) Well, 4/5 have undergrad degrees and my younger sister will probably get her Phd. While none of us are very advanced in our academic achievements, I would confidentially say that college/the working world was NOT a culture shock to us.
We didn't need our parents there to hold ours hands. I felt very prepared for college and the working world.
I guess I would caution you to not paint with such broad a brush. I have met successful home school, public school and private school individuals.
I have also met “failures” from all three backgrounds as well.
Sometimes home school is what’s best, and sometimes it’s not. But I would venture to say (and this is just my opinion) that there are a lot more children is horrible U.S. public schools who would benefit greatly from a private home education, as compared to home school students who need to attend public school.
Just my $0.02.