Well I think there is about 6 trains an hour to Liverpool, but they are all slow. And if you live on one of the diverging parts ( where they are not all going the same way ), then the frequency is going to be low.
I don't know what the off-peak demand is like there, I doubt the trains are full, but if you expect people to make changes to other trains then the low frequency is a killer for demand unless the connection points are very well coordinated.
It seems absurd to me that the best service to Liverpool is along the route which is the longest, has the most stations, and the lowest opportunity for limited stops services - the Bankstown Line.
It seems to me, they should pick one principal route to Liverpool, and make it faster. Here's some ideas.
Extend the six-track to Granville and run direct services that way. CBD-Redfern-Strathfield-Granville all to Liverpool. Run trains Lidcome-Cabramatta via Sefton as a frequent shuttle service. Continue to run Bankstown trains to Liverpool and Lidcombe.
Build a third track from Cabramatta to Regents Park. Have a two-tier service with trains stopping from Leppington all to Cabramatta and then express to the CBD in the peak direction using the third line. Service to Carramar, Sefton etc using the Bankstown line services. Consider running Granville-Cabramatta as a frequent shuttle-service.
Build a Y-junction at Glenfield and run quicker services to Liverpool in a loop using the new quad east hills line.