At most 4 to 18 private schools, scholarships are given to the best via say auditions for music, or entry tests for academic ones, they must demonstrate a talent for sport for a sporting scholarship, etc.
At my school, the kids coming up through the prep must take the same route for scholarships as the new intake at 11+ and 16+ from outside the school. So, a talented child would have to 'prove' themselves like any other, and the best
ones get it. It’s in no-one’s interests, the parents, the child, the school to
award them to anyone but the most passionate and highest achieving pupils as
they usually have so many strings attached. Music scholarships and Sports ones are really demanding, all of them are really.
A very talented child should get something, just as she would at any other school offering scholarships. Of course, there’s favourites from Prep with teachers and parents very chummy with staff, but this reflects the pupils that are talented, they become stars at the school.
So, in answer to your question, it’s not a case there’s less onus to award existing students coming through, its simply in the best interest of the school to offer them as sweeteners to the best pupils, regardless of where they come from.
And it’s probably an advantage being in a cohort that has been at the school from the Junior stage as scholarship material would have been long identified by the time of transition to 11+, this certainly happens at my school. The star at
sports, at maths etc would have long been identified and encouraged to go for a scholarship at parents’ evenings, etc.