I guess the problem I have with your argument, LegallyChallenged, is that you seem to be saying that parents who chose to educate privately because they aren't happy with the education offered by their local state school are extremely selfish and actively making Dave's chances poorer, when in fact it is more likely to be those who are still using state education but not sending their kids to Dave's school who are ruining his chances. Private school users are after all a very small minority.
I would imagine that parents who are middle class and actively involved in their kids education and due to their social conscience have sent their kids to a poor, possibly failing but local school, stepped in to try to improve it when is not achieving national literacy or numeracy standards and has other social deprivation issues when they had any choice at all in the matter are actually rather few and far between. I know several parents this year who ended up with a place in such a school and they are actively appealing against it.
It's a lot easier to have a social conscience if your catchment school isn't in special measures, or if your catchment school is at least in line with national literacy and numeracy standards.
The flaw in the argument isn't really about private schools. That's a red herring.
Let's imagine Dave's parents aren't so bothered about education and don't have a family tradition of valuing it, so they just send him to the failing sink estate school unthinkingly. Tabitha's parents are teachers/NHS workers/whatever, and they live a few streets away in the muesli belt. They were university educated and they do care about Tabitha's reading level. So they don't put down the local school as one of their choices, and Tabitha cycles to the better (but still not outstanding) school a couple of miles away. Dave is still a loser in this situation.
Likewise, let's think about Michael, whose parents are second generation immigrants living in the same street as Dave. They are a bus driver and a nusery nurse. They do value education and though they are not "middle class" like muesli munching Tabitha's parents, they also want to avoid sending Michael to the local school where the kids truant, shoplift sweets from the local shop and . So Michael goes to the local faith school, or the better school that Tabitha is going to. Either way, Dave is still a loser.
The private schools ruining Dave's chances? I think not. Look a bit closer to home perhaps?
Let's discount the traditional old school style public school users (toffs, aspirational successful builders , the nouveau riche and high level professionals) who probably do may well buy into the whole "buy your kids an advantage" or "keep out the hoi polloi" thing and assume that Henrietta's parents live near Tabitha and are of similar socioeconomic standing and value education similarly.
I think you're kidding yourself if you think that Henrietta's parents are more selfish than Tabitha's or Michael's, just because they have been able to use money to solve the problem they faced. Obviously, the option is not available to everyone, but that's life in our country at the moment I'm afraid.
Henrietta's parents should send her to the crap school, but Tabitha and Michael get a free pass? Why?
In each case it is still Dave that gets left behind, and the reasons for that are far more complex than other peoples schooling choices, and frankly, can't be solved by them.