This cannot be implemented in cricket as there are already very few teams and this division does not make any sense. However, steps can be taken to make more countries play cricket and produce world class teams.
When Jagmohan Dalmiya was the ICC president, he took a number of steps to help associate nations. His efforts were very successful, as teams such as Kenya, Ireland and Afghanistan made a lot of progress and came close to becoming full member nations. But then he was ousted and the combination of Sharad Pawar/N Srinivasan took charge (as the ICC and BCCI presidents respectively). Their term pushed cricket back by at least two decades. All the progress that was achieved during the Dalmiya era was destroyed. Not just the associate nations, but even some of the test playing nations such as Zimbabwe sank without any trace.
And it was during this period that a new law was introduced, which enabled teams such as UAE and Oman to field teams entirely (100%) comprised of foreigners. As a result teams that had native players (such as Kenya, Netherlands, PNG, Namibia.etc) became unable to compete and in turn lost their ICC funding. Some of the teams such as the Netherlands managed to survive, as they had other avenues for funds. But teams such as Kenya got destroyed completely. As long as this law is not repealed, I don't think that cricket can be spread outside the big-3.
Now the ICC claims that cricket is being played in 100 plus nations. But in most of these nations, you can't find a single native player in the playing XI. Most of the teams are entirely made of Indians and Pakistanis.