Australian Government's will pour money into privately owned grounds, I mean we've seen it with Docklands, with Kayo, even Shark Park got $9.6m to build the Monty Porter Stand.
The issue with private grounds will always be where they sit on the priority list (usually well behind public owned assets) and value they bring back to the community in some way.
It's easy for the Vic Government to justify one off investments in Docklands from an economic perspective because of all the events it holds. Kayo was able to get funding thanks to the lack of equivalent venues near by (Sunshine Coast & Perry Park are the closest), the good relationships between the Dolphins and Moreton Bay Regional Council, the small amount they were after ($6.5m) and the lure of events (NRL Games, QCup GF, Roar matches) which they previously didn't have.
Sharks have the issue that they are competing with a lot of other publicly owned stadiums in Sydney, including Kogarah up the road who are asking for more money, they are asking for significant investment and don't seem to be coming with any form of business plan to help.
The club doesn't seem to have a good relationship with Sutherland Shire Council (I might be wrong, but I've seen no one from that council push to upgrade Shark Park, offer to contribute to any funding, etc) nor anyone in state or federal helping push forward the case since Costello.