I am going through the 7+ process right now. DS1 is at a nonselective pre-prep which is academically pushy and does have a very good track record for entry into the selective London Preps.
They have several mock exams which all boys take. Those whose parents have indicated an interested in sitting the boys for 7+ entry take theirs in a more formal setting whilst those boys not sitting the exam do theirs in a relaxed manner. It is from these results, as well as teacher input, that the school advises whether or not it believes that a child would be ready to take the exam - it is not just a matter of academic readiness, but also of maturity. For those boys who are doing 7+, there is an afterschool club which prepares the boys for the exams several times a week, this way the education of all isn't at the mercy of the 40 some percent choosing to take the exam.
However, despite all the very good prep the school does, the vast majority of boys who are sitting the exam are also doing extra coaching. Some are doing Kumon maths plus tutoring twice a week! The fear is that by not tutoring, you are not giving your son every chance to get in, particularly if everyone else is tutoring. It is madness, but driven by anxiety - particularly when one hears about the 10 to 1 ratio of applicant to places at some of the schools. Crazy.
Needmoresleep comment about where the boys are long-term is spot on. The majority of boys don't move at 7+ and this is no indication of how successfully they are academically in the future. 7+ is an exam which is suited for a particular boy, but isn't the end of the academic road. DS1 seems ready, and the school tells me he is ready. However, I probably am shooting myself in the foot by not tutoring, but if doesn't pass he can try again at a future date.