The reason F isn't sold to Australia is straightforward - F yields are too low and the opportunity cost is too high.

First part of opportunity cost: yield. Have you seen what EK and SQ sell F tix for ex-Australia? In F-class land, they are extremely cheap, especially if you're comparing to cash tix to/from North America. Not in the same ballpark. Australia seems to have about as cheap F class as you can get anywhere in the world, which is saying something considering Australia is a developed country. Great for customers, but not great for an airline like CX. It doesn't serve CX well to take a plane off JFK, LAX, LHR, etc. and divert it to Sydney where they would be lucky to make 1/3 of the money for that F seat. What would you fly to JFK then. 77G? This is, of course, the tradeoff if you want to run one or two daily F-equipped planes to Australia. You'd have to swap one of the existing JFK/LAX/LHR/SFO etc. 77H frequencies for 77G, so SYD can get 77H. That would be crazy!

Second part of opportunity cost (unique to Australia): max # of flights under the bilateral agreement, as mentioned above. There is a healthy amount of Y class demand ex-Australia and the limited slots mean CX must maximize their seats/plane. This is why CX has upped the # of seats by sending 77G and 35G, starting to replace the 33Ks. 77H (the first-class equipped plane) is very premium heavy, which means less total seats. So if you insist on F, you inevitably cut the seats available in Y and PEY for CX. 77G has 268 Y seats and 32 PEY. 77H has 182/34. You get the picture. For a market like Australia, sending 77H is a bad strategy unless you can crush your yields on J and F. And "crushing" J and F yields ex-Australia - especially if you dump more premium capacity in - just ain't happening given what a competitive market Australia already is and low population country.