In addition to whatever CASA may require the more logical driver of competency checks will be the insurance companies.
The premium hike for a flying organisation who employs a business jet jockey and does not require them to undergo biannual competency training is more than the cost of such training. In addition the premium on the Directors and Officers cover will also take a substantial hike if they travel with an organisation that does not comply with industry standard check and training.
I was made aware of these requirements when one of Australia's richest men had to hire an aircraft to complete a journey rather than travel in his own aircraft. It was the insurance company who held his Directors and Officers insurance that mandated he only travel in a multi-crew aircraft and where the crew met certain training standards, otherwise no cover.