Perhaps he should also consider the role Ofsted's focus on exam and test scores has played in narrowing that contribution so much in recent years.
In a speech this week Mr Bell set out his own forthright views on citizenship and what education ought to cover in an ethnically mixed Britain. We should, he says, be positive about diversity and "intolerant of intolerance, illiberalism and attitudes and values that demean the place of certain sections of our community, be they women or people living in non-traditional relationships".
But with the "significant growth of independent faith schools", Mr Bell apparently worries that "many young people are being educated Iwith little appreciation of their wider responsibilities and obligations to British society" and this puts "our coherence as a nation at risk". Pupils of all schools, he says, should "receive an understanding" of other faiths and the "wider tenets of British society".
He is quite right in this. But why does he single out Muslim schools in particular for not doing enough to promote "tolerance and harmony" when the evidence of his inspectors suggests new Christian schools have, if anything, given proportionately more cause for concern (page 1)?
Only 3 per cent of Muslim children attend such private schools - whereas 7 per cent of all pupils are in independent schools nationally: 20 per cent of children go to Christian faith schools and half of all Jewish children go to schools devoted to their faith. Mr Bell did not concern himself in this speech with how well these far greater numbers of children "receive an understanding" of Islam.
Far from being insular and religiously intolerant, many Muslim parents choose to send their children to Church schools. It is not other faiths they fear but secular attitudes to sex, drugs and spirituality and lack of discipline and respect.
Mr Bell acknowledged that the Association of Muslim Schools is working to improve private schools. In the present climate, however, by singling out the Muslim faith in this unbalanced way, he is in danger of playing into the hands of extremists rather than supporting moderate Muslims working for greater accord.
In retrospect, he must be asking if it helped to stray so far off his beat in this speech to praise the "values and valour" and conduct of British troops in Iraq the day before a series of photographs were published apparently showing squalid abuse of Arab detainees in British custody.
Mr Bell did not even mention in his speech the Ofsted finding that learning more about cultural diversity is opposed by 40 per cent of pupils in the North of England - where religious and ethnic tensions have resulted in recent communal violence. The tolerance and harmony Mr Bell idealised does not depend solely or even mainly on changes in a handful of Muslim schools.