You know that plucking a random, fan-made picture off reddit is not conclusive evidence, right?
For starters, North Sydney still maintain their own District Rugby League competition as part of the NSWRL. So to say that Manly has the catchment from North Harbour all the way to Central Coast is folly. Secondly, it's only in recent years that the Western Suburbs district has been associated with the Wests Tigers brand (Now under Wests Tigers - MacArthur district). Before that it was still a seperate entity feeding into the Western Suburbs Magpies outfit in Reserve Grade. WSM also have development teams right through the grades seperate to the Tigers. Thirdly, the Roosters, prior to aligning with the Bears as a feeder team, were backed by Wyong which feeds from the CRL on the Central Coast. The Roosters also have 2 teams (Sydney Roosters, Central Coast Roosters) in the Harold Matthews and SG Ball competitions where they develop players, as well as NS having their own team there.
Catchment and representation are 2 very different things. Every club brings players into their junior development systems from outside the catchment area at a very young age to develop them into the players they want for their club.... because they see potential in them.
If anything, South Sydney has one of the smallest catchments in Sydney.... but guess what, they get players from outside too. They also source from the QRL/BRL as well. Any kid who dreams of an NRL career isn't going to knock back a career opportunity just because the club that comes knocking isn't representing their local area. It's an opportunity to develop and have the career that they want.