I don't know a single person who has tutored for the 4+ and I also doubt tutoring would work at that age.
It was the norm for the nurseries that my DC went to and, I believe, the norm for the primaries that my DC are going to. As you suggested in a subsequent post, perhaps North London is different.
The things selective schools at 4+ are testing are the kinds of things that come from regular engagement (daily) with parents and pre-school not weekly intensive sessions.
I have a pretty good idea what questions the primaries asked during the 4+. Highgate, which you subsequently mentioned, used to ask parents to sit in on their 3+. The tutors I knew of all debriefed their tutees after the assessments and shared the types of questions with parents. And we, of course, debriefed our own DC, and shared that with our friends. Many of the things DC were asked were not things we'd have emphasized on our own had we not wanted to prepare for these assessments. Of course, I don't know how much weight the schools placed on each type of question.
Broadly speaking, my belief is that the schools were looking for children who were "well behaved" (some might say "docile"), who paid attention to what the teachers were saying (some might say "easy to teach"), and who appeared to have parents who were very supportive of their education (some might say "pushy").
I don't think reading with your children, talking about stories and teaching them vocabulary, doing puzzles etc is tutoring them though.
I agree.