I'd suggest that maybe it is a feature of Common law legal systems, where laws are developed by judges and precedent plays a huge role. The US, UK and Australia are Common Law systems. Civil law, where legal principles are codified into a referable system which serves as the primary source of law, are a lot more easily understood and handled. So maybe the former system makes legal expertise both more challenging and more necessary for lawmaking.

If that hypothesis were true, other common law states (India, Canada, Israel) should tend to have more lawyers in office than civil law states (pretty much all other industrialized nations).