I understand your annoyance, but if you were LAN, what would you do? That route is very popular, with only a few flights per week and more than enough passengers willing to pay normal fares,... why allocate more than a handful of seats to a heavily discounted fare which brings very little revenue to the airline?

I have travelled the Oz-Chile route many times over the years, way back to the 707 days, and it has always been extremely difficult to get a seat, unless booked many months in advance, even with 'normal' fares.