I agree that a grammar school system is divisive, but certainly fairer than the system we have now in many areas - let me give you our own example.
We don't live in a grammar school area. Our local secondary is a sink (think drug riddled, 30% A-C, poor teaching, high staff turnover, you get the picture).
If we were in a grammar school area the overwhelming majority of parents would let their children have a go and/or do some tutoring themselves or pay £25 per hour for a tutor for a few months. This would be within reach of most parents, high earners, middle class, working class alike.
The current situation is much more divisive as only the superwealthy can afford the tutoring for the selective indies and then commit to 11k+ per child per year. This is the reality and I am sure we are not a unique set up.
Moving to a decent comp up the road would set you back 800k for a 3 bed terrace or if you want to rent the same house you are talking £2500k per month - and even then there would be no guarantees of getting in. Of course that comp does very well - selective by postcode.
Most people cannot afford this "fair system", which is now just advantaging a very very small percentage of people who can afford the indies or 800k for a small house.