My son sat his 11+ recently and whilst awaiting results I read up a lot on various forums. I wouldn't presume to give advice to parents on whether to appeal for a place where their child didn't make the required 121 because everyone's situation is different. However, I am sick of hearing about parents who feel that paying for extra tuition should have helped their child get a grammar school place. This only adds fuel to the comments I see time and again that grammar schools are for the rich and that the only way your child is likely to pass the 11+ is to buy the extra coaching. Sometimes there are extenuating circumstances and that is why there is an appeal process. However, the point I want to make is that it is possible for a child to pass the 11+ without coaching. My son passed, in fact he sailed through achieving well over the 121 required and he had no coaching! This, I feel well and truly qualifies him for a grammar school place - but we are certainly not rich, we both have to work to pay the bills!
You're right - clever children don't need coaching. Parents have no idea whether the tuition they have paid for has made any difference or not. If it has made any significant difference, they should be very worried indeed, as they will have to go on paying for coaching right through the child's school career. All children need is a bit of familiarisation with a couple of practice papers if they are the right calibre for grammar school in the first place.