And, of course, they are right. On the other hand, the American schooling system might be the most unequal in the rich world.
About 15,000 school districts divide up the school population, and most funding is localised, so that wealthy school districts may spend up to three times as much on their pupils as poor districts. The poor districts educate the most disadvantaged and difficult-to-teach children. Even within districts, poorer children are concentrated into schools which tend to have less experienced and less well qualified teachers.
But this inegalitarian system is overwhelmingly neighbourhood based; most children attend local comprehensive schools, and their parents have no formal choice over schools. Critics of school choice, in fact, support a highly inegalitarian status quo. They also, effectively, support choice by the back door.
Under neighbourhood schooling wealthy and well-informed parents can shop around the many districts within commutable distance of their work, and buy a house in the "optimum" catchment area of the best district; their children are then guaranteed admission to the desired school. If that is not good enough they can choose to go private. Only those without the resources to move house or pay for private tuition are denied choice.
Local governments often deliberately resist socio-economic integration of housing by, for example, requiring that all houses in new developments be more than 2,000 square foot, and stand on plots larger than 30,000 sq ft.
Such developments are effectively restricted to the wealthy.
The status quo model is inegalitarian precisely because it incorporates choice through the housing market and inequality of spending through localised funding and control.
Hence the strange character of the school choice movement. Milton Friedman laid much of the intellectual groundwork, which was taken up by former president Ronald Reagan, and conservative think-tanks like the Heritage Foundation and the Cato Institute.
At the core of their proposals was the idea of the voucher; a flat-rate sum that would be given to parents to spend at whatever school would accept their child.
But the only politically feasible voucher schemes are highly egalitarian, breaking down the barriers between school districts, and imposing "no selection" regulations on schools receiving them.
So the natural supporters of the Republican Party, wealthier suburbanites are unenthusiastic. They get the equivalent of elite private schooling through their segregated state schools, and are not about to jeopardise their privileges by voting for politicians who support radical choice schemes that might give poor children a better shot at admission to high-spending schools.
Black voters, by contrast, do support vouchers. These are the people least well served by the status quo, and they know it. But Democrats oppose vouchers on principle, and Republicans know that they have only slightly more chance of winning the black vote than Ian Paisley does of becoming Pope. The voucher movement is now, therefore, pretty much dead.
Much more successful has been the idea of charter schools, on which Blair's proposed Trust schools are modelled. Charters are often run by non-profit foundations, and, though accountable to local and state authorities, have more flexibility than regular state schools.
They tend to provide small-scale alternatives within school districts and unlike vouchers their benefits extend beyond poor kids. So they are popular with wealthier voters who want an alternative in case the regular schools don't suit, but do not want anything that fundamentally threatens the status quo.
Democrats view charters with suspicion, but do not oppose them on principle. So they get less political scrutiny than voucher proposals. Some charters specialise in serving low income children, and some do so very well, but many more supplement the choice options for the middle and upper middle classes.
The choice movement held great promise to interrupt the way we do things in America.
It has not been a great success. But perhaps it was always inevitable given that it emerged in a period when all other political initiatives have been to exacerbate inequality and injustice in the United States.
Harry Brighouse is professor of philosophy and affiliate professor of education policy studies at the University of Wisconsin