There is a rhyme and there is a reason. You're neglecting race and the whole big issues of how racialized ideas of civilization and the capability to self-govern structured colonialism. Notice that the colonies that became the richest were the white settler colonies. This is no accident. Especially when you look at the relative wealth and well-being of non-white citizens in those countries (particularly indigenous peoples). White imperial subjects who left Britain (or were non-Briton Europeans considered suitably white), were given far more leeway to enact modes of self-government and were imbued with a greater sense of access to the English liberties. Also, there were often strong economic, political, and even kinship ties between the elites of the white settler colonies and the metropole.

This was not the case in colonies like India and most of the African colonies. In those countries, white colonists were minorities and local, native majorities were systematically kept from major positions of political leadership and local traditions of rule were disrupted and discouraged. Not to mention that the wealth that accrued in those colonies had a habit of heading back to the metropole because the major industries were British owned. Put all of that together, and you have situations where the white settler colonies were provided with significant legs up when they reached independence when compared to the non-settler colonies.