I see two things feeding USA soccer's recent improvement and carrying it into the future:
1) (Legal) immigration and sheer numbers. We're a country of almost 300 million people from everywhere, and there are bound to be good soccer players in there. I'm not even talking necessarily about immigrants themselves, but second- and third- generation Americans raised in that tradition.
Look at the Team USA roster. Based on the admittedly unscientific process of skimming surnames, it's a melting pot of a team.
Of course, that can also work against us, as a lot of players who live in America choose to invoke another citizenship because it's easier to make the team elsewhere. The best analogy I can think of is to tennis, in which pretty much all the top players from every nation hang their hats in Bradenton, Fla.
B) A growing farm system. It's a common misconception in the rest of the world that Americans don't like soccer; not so. More kids play youth soccer than baseball or softball, and an ever-growing number of those kids stick with it in high school and college.
It's just that Americans don't like to watch soccer, which I believe is because we can't get behind any contest that can end in a scoreless tie. That smells too much like communism. If no one can score in the alloted time, then they can just keep playing until someone scores or someone collapses.
Lots of kids are playing, but we need a real farm system. College ball is not the answer and Bradenton is too small for our entire country. Each MLS club needs to develop a local farm system.
This perhaps sums up Australia's attitudes towards soccer too. (And they also call the sport soccer as well since they have a separate sport called Australian Rules Football). They do have a government/socialist type of solution of training young stars: provide government money to tertiary-like sports institutions (in a sense, they are like alternative universities) to train different sportsmen.
In this way they have groomed a few soccer stars, and in fact just as you pointed out, not a few have decided to represent the country of their birth or their dad. For instance, half of Croatia's squad have Australian connections, and Christian Vieri grew up in Sydney. The system also extends to other sportsmen like swimmers - remember Ian Thorpe?