Used essentially by SA to guarantee games with England and Australia (all generally white teams at the time). And then the boards basically picked and chose teams to join 'the club' on reasons not really relevant to cricket, which doesn't seem like the greatest idea for a sport to grow or even for the boards to earn money in general.
I blame it more on the fact that the teams in question and others in the past weren't really part of the main circle and have since generally found the path to it being blocked and undermined by a bunch of BS. You can't really tell me that having more competitive teams in various formats isn't going to generate interest (and money) when they play with the main sides in series and tournaments. And I don't feel like T20s are the big boogeyman hurting Tests like some of the sentiment seen here and elsewhere. IMO it's more to do with the conservative mentality running the show.
There is some truth in this. South Africa were behind the formation of the ICC in 1909, wanting fixtures as part of a Big 3. Australia were opposed. Britain was keen to mine for South African gold and other minerals. The South African government needed British investment. This was the sole reason behind The Triangular Tournament of 1912. No cricketers thought it was a good idea. It was also the reason why early SA v E matches were wrongly awarded Test status in retrospect.
MCC limited the ICC (Imperial Cricket Conference) to the empire to maintain control. India, New Zealand and West Indies joined in 1926. Nobody outside the empire was interested anyway. The Australians toured North America in 1932 with Bradman averaging 100. Locally the tour was viewed as a curiosity, nothing more.
The three ICC founder members received two votes each, other members one. Ceylon were refused membership in 1946, Pakistan belatedly accepted in 1952. Pakistan railed loudest against the status quo, supported by India and West Indies. New Zealand supported the founder members. The main objection was the Test fixture list, still monopolised by England, Australia and South Africa playing each other.
Sharpeville in 1960 and South Africa's subsequent withdrawal from the Commonwealth widened the gap between white and non-white cricket administrations. Under the ICC constitution, South Africa were expelled from the organisation and from official Tests. But the white nations kept playing them as if nothing had happened, until forced to stop by protests within their own countries.
Today's Big 3 exercise a similar monopoly on power to the 3 of the first half of the 20th century. India has replaced South Africa, and has also replaced MCC as the major power-broker. The IPL has replaced the County Championship as cricket's bread and butter.