How on earth would you 'ban tutors'? You'd have to make all private tutoring illegal and knowing how good governments are at creating unintended consequences with legislation, that would inevitably catch in music lessons, sports coaching, home education, Kumon maths & english...
I attended and now teach at a selective grammar, in one of the areas of the country where grammars educate a significant proportion of the children. The school now draws students from a much wider geographical area than in my day and it's easier for parents to find out how the system works thanks to the internet. I know a lot of people (including apparently most of the teacher training establishment) really hate grammars and everything they stand for but is selecting by parental income (independents) or house price (popular comprehensives) better?
I find it bizarre that the same people who will unthinkingly accept that a top football team or a West End show should select entirely on talent think those principles fly out of the window when it comes to an academic education. The brightest children (however you define them) are not going to achieve their full potential in an environment where it is seen as bad to be clever, they are socially ostracised and they are not challenged. I am not saying that that environment has to be a grammar but it's evidently going to be harder to achieve in a school with widely mixed abilities, unless you have a grammar-stream, in which case why is separate education within the same building so much better?
Meanwhile the independent schools I've visited are packed with the children of the aspirational, ethnic minority, middle classes...