Really? Every state I've ever dealt with has had busing for both public and magnet schools. North Carolina was huge about that sort of thing especially. Is this really not a national thing?
No, I mean there is busing, but you pay. Same for private schools.
Honestly, the best free-market comparisons are those in which you can have at least some objective numbers that are hard to cheat. God knows that most reputation-based solutions are pretty easy to game and if you thought it was a nightmare when that contractor fucks up your bathroom, just imagine how bad it would be if they screwed up your kid's 4th and 5th-grade education.
Not really. Reputation is why someone chooses Google and not Bing. Reputation itself is how colleges are chosen between as well, and it works pretty well there.
Yes. But a special needs student often needs many times the resources of a normal student and frankly, I doubt any standard credit or the like is going to cover it. I just don't know how you make a remotely affordable school focusing on more than a single special need, like a school for the blind in a large enough area. And having lived with a brother with special needs that we ended up effectively home schooling, if we weren't relatively well off and have my mom basically homeschooling the entire time along with bringing in tutors and the like, he wouldn't have made it to university and that was with my mother being a homemaker. (It cost a fortune, and he still isn't properly socialized. It was basically both of their lives for 20 years just to get him through high school academically.)
First, ability to home school is part of school choice. Second, it would be more expensive (that's the point of having a niche, you can raise the price slightly), but not as expensive as it looks. See, when one deals with a problem in bulk, they can save a lot of money, and this is capitalism at work. Those tutors are a lot cheaper, relatively speaking, when they have a full time job swapping one on one attention between a variety of kids. For example, Perkin's School for the Blind manages to make it work.
Third, I think you are underestimating how much money can be saved by not bowing down to teachers unions, as the current schools system is bloated. My mother is a teacher, and she's told me first hand stories about how hard it was, not to
fire a teacher, but just not rehire. My grandfather (a former superintendent, principle, and math teacher), has similar stories.
Fourth and finally, chances are that a decent system will have grants/scholarships (both public and private) for those who need extra help, or could be propelled further with it.