The Queen had 23 Bowes Lyon’s cousins, plus another 7 on the Windsor side. Plus 4 children of her own, and she was head of state. I think she might have been a bit busy, personally.
Additonally, I have no idea why people think she had a role to interfere into another family’s decisions about their children. Particularly since it was quite clearly a family decision - Nerissa and Katherine Bowes Lyon were in the same institution as three of their cousins on their mother’s side (Rosemary, Idonea and Etheldreda Fane). The girls’ mothers, Harriet and Fenella Hepburn-Stuart-Forbes-Trefusis, had obviously decided that the Institution was the best place for five of their children. Obviously we would disagree, but the decision was made 80 years ago (when the Queen was still a child) and things were self-evidently different then. Joseph P Kennedy had his daughter with learning difficulties secretly lobotomised, for example!
Anyway, I note however that should either Charles of William seek to interfere int he upbringings of Archie and Lilibet, that will be supported by various posters here on the basis that they will obviously know what’s best for their extended family. But somehow, I think that would be different….