I reject the premise of the question that the two competitions should exist for the overall best interests of the game globally in the first place. I think that's an unachievable and idealistic goal, and that it's inevitable that the interests of the sport and bodies in each region, nation, and the IRL, won't always align, and as such we have to deal with that state of affairs.
But setting that aside, a global monopoly doesn't address the problems you bring up anyway. All that would do is give the NRL absolute power to pursue it's own interests, and as I said before, sometimes, more often than not frankly, it's interests contradict the best interests of the other stakeholders in the sport.
The best way to actually address that problem would be more commercial competition and powerful regionalised stakeholders, not less. Take NZ as a single example; it'd undeniably be better for the sport both in NZ and globally if the NZRL was capable of supporting it's self and wasn't effectively beholden to the whims of the NRL.
Sure American Football's situation globally works out great for the NFL, but the NFL isn't the be all and end all of American Football and never has been. Their power and monopoly has stifled the growth of the sport both internationally and within the USA for generations.
Go and ask the multiple attempted competitor, minor, and spring leagues, like e.g. the AFL, USFL, XFL, etc, etc, what they think of the NFL's monopoly and anti-competition practices.
Go and ask the players and union what they think of threatening to strike being their only real bargaining chip in negotiations with the NFL and owners. While you're at it ask them, and all the players who miss out on the relative handful of NFL contracts, what they think of the lack of opportunities in their chosen profession because of the NFL's anti-competition practices.
Go and ask the international bodies and leagues, such as the IFAF, CFL, X-League Japan, LFA, European League of Football, etc, and their multiple predecessors and other governing bodies, what their opinions are of the NFL's monopoly and practices. May as well get their players opinions as well.
You'll find that most all of them are disgruntled with the situation and NFL's attitude, and have very good reason for being so. Most of the major individuals will have first hand experience of being personally bent over by the NFL repeatedly, and most of the leagues and bodies have regularly experienced corporate espionage, sabotage, and direct attacks on their businesses and operations from the NFL, and all at the expense of the best interests of the sport itself.
So yeah, following the NFL's path would be a terrible outcome if the best interests of the sport as a whole is truly your aim. FIFA and other bodies corruption aside, soccer and cricket are probably the two biggest team sports in the world for many reasons, but the devolved powers and relative independence of each body and league within the sport is a major reason why.
None of that requires a monopoly, and if anything a monopoly makes it less likely to occur, not more.
TL;DR, free-market economies work LOL.
