Let me start off by saying I'm a lot younger and so was not alive before the joint venture occurred. My team is and always will be St.George Illawarra. However, the reason I support the Dragons is because I have a parent who supported St.George, so if anything I would have been more on the St.George side. In no way am I biased because I'm an Illawarra Steeler. I'm a St.George Illawarra Dragon.
So, with that said, I'll argue firstly what Kogarah supporters? Our round 3 game against Cronulla this year at WIN in horrible conditions still saw more attendees than our Norm Provan memorial match (played in immaculate conditions) at kogarah. WIN gets better crowds than Kogarah does, simple. If supporters don't want to go to Wollongong to watch the Dragons play, that's there choice, but I don't think the club will suffer too much from their absence.
Secondly, Kogarah, given where it is situated, will never get a significant upgrade. We need a stadium worth being proud of. Not one where you can smell the toilets from your seat. The fact is Kogarah is outdated but without hope of a significant upgrade. WIN is outdated, but situated where a significant upgrade can take place.
Regarding the team song. It's also outdated, divisive, and in my opinion plain embarrassing. Who cares if most other people don't know it? At least it's ours. The Roosters song when they run out and win for example, is phenomenal, and every roosters fan sings it loud and proud. You mention clubs that have their own songs having no soul. The Roosters, Storm and Panthers have arguably the most soul out of any other clubs in the whole comp.
To finish off, let's be reasonable and remember the St.George side was falling apart. They needed Illawarra as much as they needed St.George. Without the merger, considering both teams stayed in the ARL, neither would have survived.