Sure, *A doesn't have truly global coverage. But you could say the same about OW and ST. Even with CX, JL and soon MH, OW is simply dominated in Asia by *A and ST on most routes. OW is essentially only dominant in a few important international markets: the Kangaroo Route, NYC-LON and pretty much anything to do with South America. Australian domestic flying is not nearly important enough to make or break an alliance; I don't understand the jealousy some *A flyers have over QF's membership in OW. If you need to fly domestically in Australia, fly QF. If you just need to get to Australia, NZ and SQ fly to plenty of Australian destinations. As for ST, they were utterly hopeless in South America until the recent addition of AR, but I'd still rather be a *A flyer if I needed to get to South America from Europe/North America than a ST flyer because of AR's thin international network.
The point is, I think South America is big enough and important enough for *A to make it their priority to crack into OW's dominance in the region. However, AV, CM and TA are perfectly good airlines and for now we still have JJ so things are not as bad as some would make it out to be. I'd also like to see Middle Eastern/Russian airlines joining, but for now at least *A has TK which has a great route network into the ME/CIS. I'm not too particularly concerned about domestic Australia or even domestic China where *A lags behind ST because they're just not that important.