But the Queen was very young, her children were babies when she took the throne, she had her mum, sister and her cousins (Kents, Gloucesters, and Princess Alice too??) to give her a Senior Team of about 7 royals plus partners.
OK there was a time when that Senior team were still working and slowly handing over to the Queens children.*
It should be remembered though that the Queen’s cousins weren’t all full time royals at that time - they are all a bit younger than her so mostly replaced their parents when it was needed.
King George V, Queen Mary and Edward VII, then the Duke of Kent, were all full time royals in 1936. By 1942 two were dead, one was an ex-King and one a retired Dowager Queen.
Her team when she started was herself, Philip, her mother, her sister, Princess Mary, the Duke & Duchess of Gloucester and Princess Marina.
The council thing that Andrew and Harry are about to be bumped off needs 4 people. In 10 years William could be looking very lonely meetings for one!
The York girls being Counsellors of State won’t be an issue. It’s an occasional admin job basically. And once Charles is King Camilla can be added, then when William is Kate can be.
One of the Queen’s early CoS’s was her cousin George Lascelles, then Earl of Harewood. As a son of Princess Mary he was way down the line of succession, but he was old enough.