PhD, well said and ??
It's easy to assume that a tutor is someone who will (be able to) teach/ pressurise a 3 year old into attaining a set of skills that have not yet been achieved. On the contrary, a tutor cannot affect a very young child developmentally a but can introduce both parent and child to activities across the range of skills that may come up in assessment. Whether or not these skills are going to be assessed, they are skills that will inevitably prove to be useful and lay complementary foundations for a child who's about to start primary school.
The government has put so much pressure on nurseries and Early Year settings not to formally teach letter sounds, handwriting (how to hold a pencil, name writing, letter and number formation, etc.). Typically, these are amongst some of the skills assessed at 4+. Instead, nurseries have been encouraged (by the Government and OFSTED) to focus on child-centred play and learning through play. Invaluable, but often not enough to lay foundations for good habits (particularly with handwriting grasp) that will support them as they begin their primary schooling. Perhaps this is why many private schools assess applicants.
Parents who have the ability to support their children in these areas, but who are relying on nurseries to do so, are not surprisingly disappointed. Many mummies work and/or do not have the knowledge or confidence to carry out these tasks with their children at home. A tutor can offer simple guidance, structure and reassurance as to which areas and which activities to play with / 'work on'.
The more formal skills CAN be introduced with a 'playful and fun' approach. Children tend to love them! It's also really useful to identify those areas that are particularly tricky for a child (and to bear these in mind as they develop, encouraging good habits and having our eyes open to possible difficulties) as well as to note individual strengths. We rarely get to hear such specific feedback on our young children.
An honest tutor wouldn't guarantee that a child would be offered a place as a result of practising these skills. So much is affected by the natural ability of each individual as well as by their their personality, working memory, coordination, phonological awareness, verbal ability and vocabulary, ability to follow instructions, confidence, etc.
Assessments are certainly not looking for children who can tick all the 'skill boxes' but who can't recall or follow a set of simple instructions. Good nurseries are really helpful in terms of providing children with the opportunity to develop many of the social skills involved in schooling, etc.