Think carefully , is your child naturally capable or just coached? You are doing them no favours if they are just coached to pass.
I don't believe you can coach a child to pass the 11+, who doesn't have the innate capability of passing the 11+. You can teach technique, teach them those parts of the syllabus their school may not have covered, maybe tweak a few marks here and there, but you can't tell me that you can take any child of any ability and get them through with tutoring? That would mean that no tutored children ever fail the 11+, and that just isn't the case.
Of course with any pass mark there are going to be those who just scrape in, and might struggle (though most do not), but that would happen with or without coaching.
Coaching/tutoring have become such pejorative terms nowadays. Only in connection with the 11+ is there ever the proposition that children should go unprepared into an exam.
State primaries have no interest in whether or not their pupils pass the 11+. That's why many parents turn to tutors. When the results come out, children at my son's school are told that they are not allowed to mention them. Private schools, on the other hand, teach to the 11+ because that's what the parents want. That's where the big 11+ divide really lies.