The two are not mutually exclusive. A ban would be an important stimulus to improving state schools, because of the pressure that all the erstwhile private school parents would then put on the government, local authorities, the Department for Education etc.
As long as the elite can just opt out...
I disagree with your first point. The point is not that the extra 7% would make the difference, but that the rich elite, once prevented from siphoning their brats off into the private sector, would put huge political pressure on the state to improve the quality of (and expenditure on) the state...
Alan Milburn (who led the commission that came out with this report), is absolutely correct in my view in identifying some of the causes of inequality in British society, and it very was nice of him to take some time off from his directorships of the private sector health companies currently...