For major events they run trains direct from the CBD to Olympic Park with stops at Strathfield and Redfern. This is the one I use as I come from south (usually I change at Redfern). Again I'm not sure why you think its poorly serviced by public transport. It's better serviced than the other Sydney Grounds we play major football matches at. I was at all our home games in round 3 and the Sydney and Canberra games in round 2 and although we didn't have a game at Homebush I reckon its as easy to get to via public transport as any venue we used (admittedly I stayed within walking distance of Adelaide Oval and AAMI Park so didn't use PT at those venues. Parramatta Stadium may be a bit easier now that the light rail has opened if you don't like walking from Parramatta Station.The dedicated train line takes you to Lidcombe. You then need to get to Strathfield to head north. If it was part of a connected line. i.e. Lidcombe to Concord West or Rhodes it would be ideal. As it is except for major events it is awful to get to. Even when the Sydney Metro West connects to Sydney Olympic Park it will only connect to North Strathfield - not Strathfield.
As for the Asian Cup - it is a bigger tournament that it was in 2015. Why would the FA forgo 20000 to 30000 tickets per game to play at AAMI rather than user Perth or Brisbane. Even Newcastle has more seats in a much smaller population base but close to Sydney is more likely.
The Asian Cup is now a 24 team tournament with lots of games. There may not be a stadium in Melbourne to host the semis and final but AAMI Park is adequate for all other matches. If we ever host another we will likely need to use all those stadia you mentioned. Your wrong about Newcastle. It has less seats than AAMI Park. Last Asian Cup it operated at a reduced capacity because the hills at the end were unable to be utilised. The semi final involving Australia there had a crowd of 21,000. There are plans to build stands there in the future but we will wait and see if that ever happens.