So basically only taking posh fee paying school kids I see
Several reasons for that:
1. Public schools take rugby seriously. My son is at a state school and rugby is a 1 hour a week after school club. They played 4 matches (total) during Y7 & Y8 and then it stopped. I helped out with a bit of coaching and there is plenty of raw talent there, but by Y9 only 5 boys out of 150 play any rugby at all and that's club rugby. When they did play it, rugby was once a week; at a public school like Cranleigh it's three training sessions a week plus a match. (In fairness, my son's school has produced 3 premier league football players in the last 5 years).
2. When you compare public schools with the few state schools that do take rugby seriously, the resources of some public schools mean they can develop the players far more. My son's school has no rugby pitch, no floodlights & only 1 teacher with even an interest in rugby. By way of contrast, Cranleigh supplied 2 of the 3 boys joining the academy. Cranleigh has 13 pitches, including 1 that is "international standard", two gyms, astro training facilites and a full time DoR. I saw an advert for a part time video analyst for a public school in the Midlands. Hampton School's U16s had a pre-season training camp in France. State schools can’t compete with this.
3. Public schools can take rugby ability into account when they select. I was at Trinity School in Croydon on an RFU course and the school were hosting a Sunday morning training session for Rosslyn Park U11s (IIRC). Any stand out players could be invited to apply. State schools, even ones that specialise in rugby, aren't allowed to do that. If you're a very promising player at 16 at a state school you'll probably be offered a scholarship to a public school, as Somardino notes. Kyle Sinckler going to the sixth form at Epsom College is an obvious example.
Whether anyone likes any of this or not, it explains why it’s likely to be rare that Quins recruit a child into the academy from a state school.