Since the sentence you've constructed intends to contrast the behavior of Aussie's who've gained international notoriety and the behavior of Aussie's whose fame exists only within their homeland, it seems preferable to simply state your distinction on those terms. After all, since contrast is basic to your construction, calling one group meaningful implies that the other is not. And I doubt that's built in, really, to what you're meaning to convey.
Here's what it looks like you intend, if you'll allow for the split infinitive:
As soon as mega-talented Aussies gain international fame, generally speaking, they seem content to abandon our shores and leave Australia in the trusty hands of celebrity hairdressers and celebrity cooks.
Beyond this, what you're asking for somewhat eludes me. Are you looking for a title, a phrase to use in another sentence referring back to this one, a replacement for the term meaningful socialites in this sentence, or, more broadly, just a way to talk about the phenomenon?