It's worth reflecting that a significant proportion of Indian politicians (including Nehru) wanted nothing to do with the Commonwealth and only agreed to join when it no longer required acceptance of the monarch as Head of State. To say they "flocked" is over stating it a bit. They saw the benefits in a body of mutual cooperation and interest based off existing ties in trade etc that had been built in the empire, but they explicitly didn't want to retain any sense of that being connected to Britain as a 'mother nation'.
Exactly. Also the US never wanted to join. Ireland quit in 1949. South Africa, who should never have been members with an Apartheid regime left of their own accord before rejoining.