It isn’t true that “every child needs a tutor.” It certainly is true that “every child can benefit from some 1:1 tuition.” Anyway. Here’s how it is…
If you are in a grammar school area, eg Kent, then most children in the State sector who want a grammar place are tutored to help them pass the 11+ exam. This is because State Primaries do not teach them about the exam format, or even some of the topics that the test contains! Non-verbal reasoning, for example.
Some children are tutored by their parents instead of by a paid tutor. I have not heard of any children who passed without any 11+ exam preparation at all. I do know several children who passed the 11+ without a paid tutor, they learned how to pass in weekend tutorials with their parents.
Whether paid tuition or parent tuition, it’s definitely not true that this tutoring is usual from Year 3, in fact many tutors recommend tutoring in year 5 only, to prevent the children becoming bored. (That said, the best tutors can have waiting lists from year 3.)
Seperately, many State Primaries are really struggling with staff and funding shortages and also pupil behaviour post-lockdowns, and so are unable to give much attention to the best behaved children, so even forgetting about whether you’re in a grammar area, a tutor is so beneficial for children at many struggling schools.
If you are not in a grammar area, and are lucky enough to have a school that isn’t struggling, then your child doesn’t need a tutor (unless you want one… 1:1 tuition is always beneficial).
At Prep schools the situation is different. Some Preps teach children how to do the 11+ content and format, others do not. Even where (as at my Prep) the school does teach children non-verbal reasoning etc, many parents who have money to spare choose to have a tutor, in the same way that they may chose to spend money on swimming/gymnastic/horseriding lessons, etc. This is often contagious, eg one parent hires a tutor because their child is a maths enthusiast who wants to do more advanced maths than the school/parent are willing to cover, and then their classmates’ parents hear of this and all panic-buy a tutor too.