Sport in the US definitely has a history of splits/rivals popping up, the NFL have had the AAFC and XFL, MLB had the AL & NL at one stage, NBA had the ABA as a rival, NHL had the WHA pop up and I'm sure there are plenty of others that have occurred as well.
Unlike these other sports, RL in the US doesn't have the money, players or reach worthy of the level of infighting that occurs.
Since the 2000s we've had the USRL v AMNRL split, then the AMNRL v USARL split, then the NARL v USARL split and now its CRL v USARL v Unaffiliated clubs.
Honestly, I wish the IRL would fo something similar to Tonga and install an independent committee for the national team and then from a domestic perspective, divide up the country and let each of these independent leagues just run themselves.
The NERL can have the North-East, the USARL in the South East, PCRL can have Southern California as they are based between LA and San Diego and give the CRL the rest of California + Nervada and then Utah can be a game of roshambo.
It's a big country and the reality is the officials in one corner of the country barely have the resources to look after their little patch, let alone be trying to do anything anywhere else effectively.
League as well is unlikely to ever establish a decent presence in the US until it has more regional based competitions anyway.