In my (somewhat limited, I don't have kids, but went to school in towns with many options for private education) experience, private schooling in the US at every level is prohibitively expensive for all but the upper-middle class, and even then is usually a significant financial burden.
It really depends on your social circle. When pricing private schools, you need to realize that the very top will always be crazy expensive, because the very richest parents are paying whatever it takes to make sure their kids only interact with the kids of other rich parents. Whether this is effective is debatable, but enough do it that you have to slice them out of any analysis.
Private schooling doesn't have to be crazy expensive. 15 students in a room paying $500 a month is $7500 in revenue, and with roughly half going to overhead that still leaves $3750 going to the teacher, which over 10 months is a little less than the average US wage. If you make the workplace pleasant enough (such as not requiring teachers to have co-workers who cannot be fired) you can fill the roles.
That's about 5K a year. We can probably go down a huge rat-hole of whether a middle-class family can "afford" 5K, but I don't think it crosses into the lines of "prohibitively expensive."
There are also Catholic schools, which used to be much more prevalent, but they still exist.
My mistake in wording, I didn't mean that it was prohibitively expensive by necessity. It seems that education costs are artificially inflated in the US at all levels. I agree completely that education doesn't need to be expensive to be effective.
You can definitely find expensive private schools in every area. In my experience you can also find decently priced ones.
For my oldest we've moved through public, home school, private, and back to public over the years, trying various things. I have a criticism of each of them, and while we may have chosen the "wrong" private school, but it wasn't price that had us choose there.
