We've hit the problem that the NRL was trying to avoid back in 2000. For their ideal comp of 26 weeks, you need either 14 clubs for the double round-robin, or a single round-robin of 27 with teams alternating home and away games every other season.
Moving up to 20 clubs
If the NRL are still allegedly keen for 20 teams in the future (which was EXACTLY what they said was unacceptable 3 decades ago), you either go to 19 rounds or a conference system.
19 round proposal
Instead of each team losing 5 games a season, this could be alleviated by the introduction of a secondary or complimentary competition, such as a knockout or "challenge" competition to fill the void every few weeks.
A possibility would be 4x pools of 5 teams, therefore 4 round-robin games and 23 played by each team (so far). Semi-finals for the top team in each pool facing off, followed by a final leaves a maximum of 25 games per team before the Finals Series, a maximum of 29 first grade games in a season for the Premier and runners-up or an increase of 1 on the current 24 games + 4 weeks of finals.
The main challenge would be the need to balance home and away games, with the possibility of some teams having an extra one per season, but could be fixed with strategic scheduling each year.
2 x 10 Conference system
Without resorting to the massacring of clubs, the next logical step is to segregate teams into conferences to reduce the need to play *every* team twice whilst still increasing fairness. This has its own level of complexity and leagues like the NFL still struggle with the increased complexity.
Two pools of 10 clubs gives the possibility of 9 or 18 games (single or double round-robin) within a conference plus 10 or 20 games outside.
All of the current NSW teams (excluding Canberra who I wouldn't consider part of that) number up to a 10 team conference, with room for 3 new clubs in the non-NSW conference.
The most fair solution would be a double round-robin within your conference (18 games) plus a single interconference round-robin outside (with alternating home-away every other season). However, this leaves each team potentially playing 32 games should they make the Grand Final which is 4 more games a season than currently.
Then you need to factor in players who play Origin, All Stars, trials, WCC, etc. and the RLPA would (rightly) shut that s*** down.
Is 18 teams (2 x 9 conference system) the answer?
I've long thought that a conference system of 2x 9 team conferences is the optimal solution for fairness within the NRL's current limitations.
Theoretically, this would leave a double round-robin in conference of 16 games played with 9 interconference games in a single round-robin for 25 games total.
However, the season would be longer given the need for each team to have two byes in conference given the odd number of clubs, creating a 27 round regular season.
In the realm of the NRL, this is nearly "theoretically perfect" except for 1 detail: where do you draw the line between conferences?
With the current teams, Canberra (as above) and Newcastle would need to be included in the non-NSW conference, with only 1 new club able to be admitted in that conference, with the NSW/Sydney conference locked forevermore.
To geographically or not to geographically conference
The easy solution is to create a Sydney/NSW conference and an "everyone else" conference. It also creates something that I believe would enhance the season and solve a few headaches the NRL faces regarding Grand Final rights: a Sydney final, a "national" final and a brand new Grand Final.
Imagine this: Souths and the filth playing in front of 83000 for the "Sydney" premiership, with the Dolphins and Broncos playing for the "non-Sydney" (better name required) premiership in front of 53000 at Suncorp. And that's not even the Grand Final, which is the next week in front of 110000 at the MCG. If your mouth isn't watering at the possibility of nearly 250000 across 3 games, check your pulse.
The biggest problem with this is that the Sydney teams would only need to travel significant distance once every 3 weeks or so, while the others would be constantly travelling. In a European nation, it's probably not that bad, but down here it's a big problem.
Imagine travelling from Perth to Townsville or Auckland (possibly within the realm to 3 weeks). Ouch. Especially when half the Sydney teams will probably be playing at Parra or Allianz in the near future.
If you don't go the geographic route, you could reseed each team each season, but that opens up yet another can of worms re: fairness.
Is perfect possible?
If you choose to ignore certain parameters, of course. Duh.
The RLPA, clubs, officials, fans, administrators will always find things that don't work for them. This is part of being in a complex system where slight changes have massive knock-on effects down the chain.
I really can't suggest something that would "just work" - if I could it would most likely already be implemented and I'd be copying it verbatim.
The NRL have the very unique challenge of a physically taxing and exhausting sport, a vast nation where travelling is arduous and a competition that is challenged by every single variable.
If the NRL was strictly NSW or Sydney, this is an easy problem to solve, but the very nature of the NRL requires crossing thousands of kilometers and, potentially, seas and oceans on a weekly basis.
Is there a better system than what we have? Probably. Do I know what that is? No, but I do have some ideas. Hopefully, someone will have something similar and be able to make something even better.