Let me suggest another reason that I don't think is in general the case for why people hire tutors but may be why when they do hire tutors some people are willing to pay so much: Having private tutors for children is a status symbol in some contexts. And that status is higher if one is paying more for the tutors.
That said, I suspect that in actual practice your first four reasons are likely the main causes.
JoshuaZ:
Having private tutors for children is a status symbol in some contexts. And that status is higher if one is paying more for the tutors.
Is it really a high-status signal? To me, it primarily signals that they have low-ability kids who are finding it hard to keep up with the educational expectations imposed by the social class they were born into.
Maybe my social radar isn't well-calibrated in this regard, but it has always seemed to me that successful kids are expected to breeze through school with their own smarts and abilities, while extra tut...
It's an anecdotal commonplace that rich parents in places like Manhattan are willing to shell out a colossal amount for their children's tutors. Most recently I heard about a math PhD student at an elite university who's getting $500 an hour to tutor high school kids.
Now this makes me wonder: why do tutors get paid so much, but not teachers? Why isn't there a private school somewhere, full of elite superstar teachers, getting paid colossal sums? Why isn't there someone trying to lure young people into being very well-paid schoolteachers instead of professors or hedge fund managers? If some parents have the extra resources to spend on their children's education, why is that money going to tutors rather than schools?
Some hypotheses that came to mind:
1. One-on-one tutoring really is the form of learning that gives you the most bang for your buck; the marginal dollar is best spent on getting a better tutor because tutoring is more effective than school.
2. The marginal dollar is best spent on getting a better tutor because tutors are independent contractors. Switching your kid's school is a big change for the kid, and a discrete jump in price, but getting a new tutor at slightly more cost is easy.
3. Something about the rules of teacher's unions prevents a few "superstar teachers" from being paid colossal sums.
4. The sort of person who becomes a $500-an-hour tutor usually has a background in something other than education, and isn't credentialed to be a schoolteacher, and perhaps doesn't want to teach full time. You could get him to tutor, if you paid well, but you couldn't get him to be a full-time teacher without an expenditure beyond the means of even the wealthiest parents.
5. Parents are using tutors to improve their children's grades, not their education. Putting that same money into the kid's school wouldn't improve the kid's grades relative to his classmates'.
Any other ideas?