I'm not entirely sure what you're advocating, because what they're already doing is having frequent all-stations service that cover the inner suburbs and the city (between Bondi Junction and Hurstville). The intention is one changes at Hurstville if they need to travel between north and south of Hurstville but not to/from the city.
If what you're advocating is a service that only travels between Sydenham and Waterfall/Cronulla, there are multiple problems with that. Firstly, the people that travel within that area are probably a minority so it will be very lightly loaded compared to trains that actually go to the city. Secondly, such a service isn't made of air. It is occupying a space in the corridor that could actually be taken by a train that does go to the city. Third, I don't know how you expect a terminating service to be run to Sydenham considering all six platforms are used up by trains that aren't terminating in peak hours.
The fact of the matter is that the entire network is based around an idea that people who live further away from the city should have services that skip stations closer to the city because these people have to travel longer distances and generally have longer travel times. It's a pretty fair principle, isn't it?
If you're suggesting a reduced fare because you're travelling between inner suburbs, why not a reduced fare if you have to catch more than one train to work? Why not a reduced fare because you live on the South Line which has fewer trains than the Illawarra Line? What about if you live on the Richmond branch of the Western Line? Or the Carlingford line?
Also consider for example the stations of St Peters and Erskineville which actually do have platforms facing the Illawarra Line but no services. Taking your theory, why doesn't the Illawarra Line also stop at those stations? What if a person who lived at St Peters travelled to/from Tempe for work and has to therefore change trains at Sydenham?
Should all the trains on the Illawarra Line also stop at St Peters or Erskineville as well? Should they get a discount because they need to change trains at Sydenham to get to Tempe?