Should they be abolished? Are they only good in theory? In reality I think they are hopeless at galvanising social mobility. I might be very wrong on this but from what I observe, they tend select supposedly clever children from not-quite-posh backgrounds, who are often trained like dogs to pass the 11+ in the first place by their ambitious, insecure, dinner-party show-off parents, and the level of smugness they can instill in some children is unacceptable. The smugness and the inflated ego then often becomes a permanent trademark in their personality, as they belittle their state-educated, non-Russell-Group-university-bound friends, which is hardly a good thing.
Instead of enabling not-stupid children from not-rich backgrounds to access the same level of education as not-stupid and stupid children from rich backgrounds, I think they tend to be dominated by kids from rich-ish backgrounds, whose parents would otherwise contemplate sending their kids to a private school straight away if they failed the entrance test, but would obviously prefer them to go to a grammar school because this would ultimately save them lots of money, so from their point of view it's worth a shot. Stuff like this irks me a lot...
No offense if you go/went to a grammar school, but like private schools, I think their existence is just another middle finger aimed at the majority of society. Apologies for the inverse snobbery, but I don't think crimes like this gets the publicity they deserve.