I think this speaks volumes about the way Clarke's batting right now. If you go back a year or two and asked anyone this question (and excluded Bradman from consideration, naturally), most people would jump on the Border, Gavaskar, Boycott or S Waugh train - getting a dour, grinding batsman to be the one batting for your life.
Clarke is not dour. He is not a grinder or a grafter who eliminates risk to bat for long periods of time. He turns games and digs Australia out of trouble while playing his shots and taking the attack to bowlers - the South Africa knock being the crucial example. Plus he alleviates the pressure while he does it, helping out the guy at the other end. It means he builds partnerships and gets the best out of the guy up the other end (200+ with Cowan).
For someone to pick Clarke to bat for their life ahead of a Gavaskar, Border or Waugh (Boycott not such a good example; he'd sell his grandmother for a ton), shows just how good a batsman he is.
Getting back to the point of the OP, one reason Clarke is rarely seen as a home-track bully is because of his technique, IMO. He isn't inherently more susceptible to the swinging or seaming ball a la Sehwag, and he's the best non-Subcontinent player of spin I've seen. His success isn't determined by the state of the pitch. While there is definite correlation between less batting success and playing overseas, I'm not sure there is causation there. Honestly, I reckon it will even itself out as Australia plays overseas over the next couple of years. His form will transfer across.