Tim -
Unfortunately, money rules the word of golf, and the foreign golfers base themselves in the US and play the US tour because of the $ $ $. Likewise, many of the PGA Tour foreign players play select events on the Euro tour for the appearance money, or because it is in their home country.
It is commonly stated that about 50 golfers have a realistic chance of winning a US or British Open or the Masters, and the Top 50 of the World Rankings are exempt from qualifying, therefore, I doubt that replacing the middling US players with middline Euro or Asian tour players would make any difference.
Playing a major in Australia would only help the Australians (or the golfers on the Australian Tour), and only those Australians that live there most of the year. A golfer playing the Asian Tour probably has conditions (style of course) closer the PGA Tour than the ANZ tour.
As for the travel angle, the top international golfers still play a majority of their golf in the US; Scott he has played in 15 PGA events, 1 ANZ event and 2 Euro (1 the British Open); Goosen 14 PGA Events, 7 Euro and 1 ANZ; Els 14 PGA, 4 Euro. I will agree with you that many of the US golfers don't travel; the view the other tours as a step down from the PGA Tour and if they have their card, why travel unless you get appearance money to do so.