No one devising an education system for an agreed Northern Ireland would have come up with the hodge-podge we have today.
What the Belfast Telegraph/LucidTalk poll shows is that most people clearly want Catholic and Protestant children to be educated together.
The poll reveals that 79% of parents questioned would support a request for their child's school to become integrated; 71% agreed that a single education system is the best way to deliver education in the future.
The current mix of arrangements is a legacy of the divided Northern Ireland out of which arose conflict and renegotiation.
Many of the old problems were resolved in the Agreement of 1998 and shortly after it. Old irritants, like questions of identity and cross-border co-operation, the nature of the link with Britain, the character of policing and even the ending of paramilitary campaigns, were tackled.
But an educational legacy from the past remains as divisive as ever. No consideration was even given to the idea of remaking Northern Ireland through mixed schooling for the two major communities. Integration was not negotiable – even when practically every other problem was on the table.
Policing was another issue that was too difficult for the parties to sort out by themselves, so the expedient of the Patten Commission relieved them of the headache and presented them with an answer they could accept, without fear they would be accused of creating it. But there was no commission to consider how we might make the most radical and crucial change to our society by bringing Protestant and Catholic children together in the classroom.
How difficult that would be was made clear just three years ago, when First Minister Peter Robinson told his party that he wanted to work for an end to "educational apartheid".
The Catholic hierarchy branded this as a sectarian move against them. They were not going to allow that there might be any good faith, or genuine hopes for a better Northern Ireland, contained in a criticism of Catholic separatism.
The state system is predominantly Protestant, not just by virtue of the Catholic Church opting out, but by its own legacy of Church schools transferred to the state on the understanding that a Protestant ethos would be preserved.
Another legacy of the conflict is the radical experiment of integrated education started by parents. This was a bold movement, but it has failed to produce sufficient momentum and many of the schools preserve a Christian evangelical culture which can only disingenuously be considered equally attractive to all cultures.
And the Catholic Church – defensive of its own system – has refused to provide priests as chaplains to these schools.
The Catholic determination to remain apart is usually justified in terms of a specific Catholic ethos that no one succeeds in clearly defining as anything but broadly Christian and concerned with the cultivation of social conscience.
Its roots, however, were in the nationalist refusal to be part of the Northern Ireland state when it was created. Catholics believed that they would not get education, unless the Church provided it. This rationale disappeared in 1947 with the Education Act, which obliged the state to provide free education for all.
Ten years after that Act, I was being taught in an improvised classroom in the damp and smelly pavilion of Casement Park, while my parents were paying into a school-building fund. No one was even making the argument that we should just let Stormont build us a school.
Ten years after that again, Catholic schools were campaigning against minority state representation on school boards as a condition of increased funding.
Today the challenge to integrate schools is enormous. The Catholic Church argues that the high level of attendance at their schools proves that people want their children to have a religious upbringing. It also reflects the territorial division of our communities and the desire of parents to have their children kept safe from the danger of sectarian strife.
The only argument for faith-based schools that the Churches are entitled to is the faith-based argument. They have no right to thrive on the segregation of communities and the fears of parents.
And, given the shock which has been caused by revelations of endemic historic child abuse in the schools, one major concern of parents is met, in part, by the demise of Catholic teaching orders.
It may be that, if those orders were still in place, the flight from Catholic schools would be a lot faster, given what we now know. What is attractive about those schools, for many, is not the religious character of them, which is hugely reduced, but their proximity to Catholic residential areas and the high marks they get.
With only 15% of the population in favour of institutionalised segregation, according to the Belfast Telegraph/LucidTalk poll, it is no longer possible to argue that most Catholics want their separate system for religious reasons.
Indeed, many of the schools found that, when they were tempted to end the grammar system, Catholic parents threatened to take their children to Protestant grammar schools for the kind of education they wanted their children to have. It wasn't religion that mattered most to them.
Ironically, the demand that the Catholic grammar system be scrapped came from the bishops. Some of those bishops now understand that a genuinely faith-based system would be a lot smaller than the current Catholic system.
There is a reason the political parties did not include the reshaping of our school systems in the Agreement talks that produced an agreed political system: they would have found themselves considering huge questions like bussing, confronting the Catholic Church, challenging the grammar system, making many enemies and getting little thanks.
They reneged on their responsibility, because the job was just too big. So it remains a challenge yet to be met if we are ever to be free of sectarianism and of history repeating itself.