"Previously communications minister, a role in which he credits himself with having turned around Australia's national broadband network . . ."
Indeed I do credit him with that - or at least give partial credit: he managed to take a forward-looking infrastructure plan, designed to create a network with provision for (and thereby enabling) growth in the future and he turned that right around. Thanks old boy.
I agree with Malcolm that "not all government business requires security-controlled email", but that does not necessarily equate to there being no risk running a private e-mail service that you use for the less-sensitive government business.
The problem with the argument is that running a private service with a recognisable address that you do use for at least some government business (regardless of security level) means that you instantly give e-mails sent from that account a certain level of credibility as coming from the Prime Minister of the the country more girt by sea than any other.
And, once you have an account that has credibility as being operated by the Prime Minister, if the server hosting that account is broken into then that gives an attacker the ability to make statements carrying the influence of the Prime Minister - at least until the ruse is discovered.
That might not seem overly problematic but just think of the recent stories of how one piece of false news can create rather large reactions in the share market. And it doesn't take an overly active imagination to think of the fall out if the account was hacked and used to send e-mails lacking the decorum usually expected of a Prime Minister. As with news affecting the share-market, such things are picked up lightning-quick and can spread a long way very quickly and do a lot of damage before anyone has the chance to get the damage control working.
And, even once it's all sorted out and everyone accepts that the comments or announcements didn't come from the PM, there is still the lingering damage from the incident being allow to occur in the first place.