Flights between Australia and SA are in extremely high demand -- so high fares and limited availability. Many wind up flying SCL-LAX-SYD as the SCL-AKL-SYD flight is sold out, for example. QF does fly EZE-SYD. However it is basically adding 50% to trip length; most wouldn't consider that on the way.
The outer islands of Fiji can be quite pristine. The main part is like Hawaii, just much less densely developed (sort of like Waikiki in the 60s, so quite nice). The more exotic islands are hard to get to, don't have daily flights and can be boring unless you are going there for specific activities like diving or sailing. Easter Island is a great destination but really difficult to get to (LA flies SCL-IPC-PPT on alternate days). Definitely not on the way to BNE.