"But grammar schools are part of the system, private schools are not." Not really. grammar schools are part of the state system, private schools are not but both are part of 'the system', rightly or wrongly.
HE isn't the only alternative - seeker could embrace the 'perfectly fine' secondary modern at which she expects her dc will achieve well at with good home support and which clearly does have at least a few of the 23% attending. It's the fact she's decided the presence of a grammar means she cannot use this school while at the same time criticising others for not using their local state schools that they consider to be less than ideal for their own dc (for whatever reason) that grates. All systems have their faults, but she only recognises the faults with grammar and private systems.
That said, I am fed up with how these threads always end up this way.