Six Dominions Rugby Headcanon:
After the end of the war in 1943, it became clear the British Empire was not long for the world without significant reform - and the reform chosen was to give greater power to the dominions while also bonding them further with economic and diplomatic ties, so they could collectively keep enough of the empire around for the upcoming Cold War. This failed. However, before it did, the Six Dominions Rugby Championship (modelled on the Home Nations) had been created as one of several great cultural measures. This did not include Canada, who weren't that interested.
For the first few years, everything went well - especially for the Irish team, who were already used to the Home Nations tournament. The Balochistan & Sindh team came up fast, 'hothoused' by the government as part of their various efforts to bond the new country together by newly-built common ties. TV ownership doubled across the dominions, and leapt among diaspora communities in Britain, to watch the Ireland-Balochista & Sindh match in Singapore.
Then South Africa brought in apartheid. The damage this did to the 'Empire and Dominions' status quo was immense, and it similarly wrecked the rugby. Protests grew against South Africa's involvement, which extended to key members of the New Zealand team and then, only a week before the tournament began, Balochistan & Sindh itself pulling out in protest at the treatment of Asian South-Africans. With one team crippled and one of the most formidable teams absent, South Africa pulled an upset win.
Things deteriorated from there. South Africa boycotted the tournament from 1950 on, refusing to be involved if Balochistan & Sindh were - and in 1954, the ongoing conflicts in the Commonwealth over apartheid had reached 'White Australia' and Rhodesia, so Australia dropped out as part of its growing closeness with Praetoria.
The Six Dominions stubbornly refused to change their name. They felt they could get the missing nations back. They didn't want to show weakness because damn it, those games were a moneyspinner. In an attempt at hardball (and to avoid "Four Dominions" jokes), in 1955 it used the South African Exiles team of political dissidents. This team, however, were crap and existed solely as an 'up yours' to the government.
After 1956, when the Punjabi Emergency forced the withdrawal of Balochistan & Sindh, everything seemed over. But remember: there was money involved. In 1957, with the Emergency done, the Six Dominions formally cast out the boycotters (even as Australia was trying for rapprochement) and inducted Bengal and the East African Federation as members, even though these weren't actually dominions. Both nations, following Balochistan's lead (now the United Indus Republic), made damn sure to build up their teams after bad defeats in 1957 and came close to victory.
By the 1959, the status of 'dominions' versus any other independent nation in the Commonwealth was meaningless and, more importantly for the bottom line, several other countries were interested in competing. In 1960, the championship was revamped as the Commonwealth Rugby Cup - and while Canada was still not interested, a Quebec team, noting how the South African Exiles had got attention, took part.