The Sydney NRL teams kind of do make it really tough on other codes though. The Swans got a nice gift from us in the 90s but haven't shown any real growth since then and GWS is struggling big time.
The Waratahs boomed after the SL war and into the early 2000s but have struggled and the A League got off to a good start but has faded.
Now that RL is getting its mojo back and some decent facilities in Sydney, the future is bleak for the other codes when it comes to finding any meaningful growth
Correlation doesn't equal causation.
The Swans started going well after Tony Lockett joined in 95, carried them to their first GF in 50 years in 96, and was the head of a team that lead the way to a golden age that arguably continues more or less to this day.
Super 12 went well because of a mixture of the novelty factor, the excitement for the coming 2003 WC, and the fact that the standard of play in RU in the southern hemisphere at the time was actually really high. It's no coincidence that it's popularity tanks after 03 when a new, incredibly regressive, standard of play takes over from the old exciting one, the WC is in the review mirror, and SANZAR proceeded to make a bunch of really bad business decisions.
A-league didn't start until well after SL, so I don't know why we are even trying to pin their "success" on SL. They also didn't hit their peak in popularity until the early 2010s, after which they made a series of really bad business decisions of their own, that more or less stopped that growth in it's tracks, but I digress.
The point is that you don't need the SL war to explain the successes and failures of the other codes, in fact Occam's razor would suggest that with the sole exception of Super Rugby (that only happened because of the professionalisation of RL) that SL had no significant effect on the popularity of any of the other codes.
Frankly, trying to blame the other codes successes and failures on SL is at once an excuse for RL's own failures and a sickening form of self flattery that suggests a bloated sense of self importance within the sport.