You’re missing the point.
This isn’t a Wests - Balmain thing.
It’s an issue of identity
Playing a few games in the area every season isn't good enough to instil any local connection.
Like I said, I don't believe "local connections" to first-grade clubs are common any more. That's an out-dated concept for a modern teenager.
It's got nothing to do with specific Tigers neglect (or not - let's not open up an argument about whether or not Tigers are actually neglecting the area).
It's very easy to prove this just by a quick survey of clubs.
Who is the Bulldog's most prominent current player? Well he's from Dubbo via Penrith. Who is the Roosters #1 player? He's a Magpies junior. Melbourne's Top 3 players, no matter how you dice it, are not from Melbourne. Titan's biggest-name signings are from Brisbane (Fifita) and Orange (Fa'asuamaleaui).
Tiger's best player is Stefano (from Parramatta) and the guy currently turning everything around (Hastings) is from Wollongong. You would have a point if you identified Doueihi as Tigers' best - an actual local junior.
Shark's star imports in 2022 are from Central Coast (Hynes) and Bega (Finucane). The Dragon's #1 paid player is from Queensland. Warrior's dynamic young fullback is also from Queensland. So is the Raiders' #1 representative prop. Jack Wighton is from Orange. Cody Walker was born in Nowra and went to school in QLD. Payne Haas is from NSW and the Broncos are experiencing a resurgence under a former Rabbitoh halfback. The Knights star fullback is a Kiwi via Townsville. The Eels halfback is a Balmain junior and their fullback is a Manly junior. The Cowboys million-dollar lock is a Tongan/Kiwi.
I can only really think about 2 current examples of truly localised players / groups. First is Manly and the Turbo brothers - legitimate family local dynasty. Though, I would argue if any other club picked up Tom and Jake as a young pair, they would be equally as wedded to that club.
Second example is Penrith. You can fairly argue that they are a very local very tribal group. However in my opinion that is somewhat separate from a specific loyalty to the Panthers and arguably unique amongst NRL clubs. My opinion is also that guys like Nathan Cleary are more loyal to their mates before the club, and Penrith have the fortune of having a boom group of juniors all presenting and playing together at the same time, not being picked apart by other clubs.
Even still - Nathan Cleary began playing rugby league in New Zealand at the age of 13 and might not still be at the club if Panthers didn't bring his Dad back. Their star backrower is a Fijian brought into the NRL via North Queensland. Their #1 prop is a Kiwi. Their representative lock is from Dubbo and the son of a former Tigers/Bears player. Api Koroisau is a Berala Bear originally signed by the Rabbits.