It is important to remember that Princess Elizabeth was, from her birth in 1926, heiress presumptive to the throne, and third in the line of succession. Her uncle, the Prince of Wales and later King Edward VIII, was unmarried and so had no legitimate heirs. So her father was next in the line of succession, with Elizabeth after him.
Few people took much notice of this in 1926 because there was still a popular expectation that the Prince of Wales would marry and produce his own heirs. There was also the possibility that Elizabeth’s own parents, the Duke and Duchess of York, would have a son. But while the couple did have another child, in 1930, it was again a daughter, leaving the line of succession unaffected.
By this time, Queen Mary had fully focused her hopes for the future of the monarchy on her eldest granddaughter. In 1930, the Prince of Wales was 36, and still a bachelor. He had an active social life, and – as his mother will have known – a number of mistresses. But he showed no interest in eligible young women, whether foreign princesses or British aristocrats.
Queen Mary was a highly practical woman, and she knew her son well enough to realise that he had little traditional sense of duty to the institution of monarchy and so was unlikely to be persuaded to marry an eligible girl for the sake of providing an heir. She recognised that there were therefore high odds that Princess Elizabeth would ascend the throne in due course and Queen Mary was determined that she be fitted for her role.