The widening of the gap isn't really grammar to private, but the loss of good teachers to private from grammar that trickles down to comps and uppers.
The incentive I think is primarily wage, my friend is a physics teachers who sold out to private after just two years in state schools, the same amount of time she spent doing a government funded transition course with a 2k top up. She was offered ?k more to move to a very small girls school in a lovely location, but yes she does get stick from pushy parents.
I have to say working at stowe must be rather lovely. (Well if you remove all the teenage boys anyway)
I suppose just like consultants, doctors and nurses, until we pay more for the state sector they will move across, but the nation cannot afford to pay more, so the wealthy few benefit and stuff the rest of us.