The reason why you don't want the brightest kids being syphoned off, (and at 11 that skews very heavily towards kids who come from settled, middle class families) is that it has a knock on effect to the balance of the state schools left behind.
The private schools wants the brightest kids, not because they want to make a difference to society. They want them because having bright kids pushes up the standards of everyone, and brings up their exam results, helping them attract more rich kids.
It's not a race to the bottom if you want to raise standards throughout the system, instead of giving an extra boost to the kids who least need it.