Two different groups of children, who need different forms of attention. The anti-grammar brigade keep getting them mixed up.
First group, the kids from poor backgrounds, but who actually want to do well and achieve a good education and have parental/family support.
Second group, the kids from poor backgrounds who don't have any aspirations and are held back by poor attitude from themselves and their parents/families.
Two different problems needing different solutions. More grammars would help the first group as long as there is also some encouragement from primary school (not the all too prevalent current issue of teachers themselves being anti-grammar on ideological/political grounds). More grammars wouldn't help the second group because however much "help" is given by the schools etc., if the parents don't give a toss about education, the kids don't stand a chance however much external help they are given.
It reminds me of a classic comment in the "Kes" book (ironically an anti-grammar book written by a former grammar pupil - typical pulling up the drawbridge behind you!), where Billy wants to borrow a book from the library but he needs a form signed by his mother, and he knows his mother will never sign it! Just the same as the current "problem" families who don't care about education - even if the schools managed to motivate a bright kid from a feckless family background to apply to the grammar, would the parents even fill in and sign the application form if they were against the perceived "posh" education.
As I say, two different groups which need different attention.