A decade or so ago, UA was often the cheapest option LHR-SYD (sometimes ludicrously so), probably in reflection of it being a bit further, and that it's less convenient because you have to clear immigration and customs.

I know that the big six are now the big three, and that competition, especially domestically, isn't what it used to be. But all three of them (and Virgin) now serve SYD, unlike in the day of the UA/QF oligopoly. So why then don't they flog any unsold seats Europe-USA-SYD at competitive fares (they're currently about 50% higher than connections in the other directions)? Are they really that busy?