"A democratic republic"

Luke Whittington writes about a 'democratic republic' at On Line Opinion:

The motivations for becoming a republic are many, but the most important has always seemed to be that Australian culture and politics are, at their best, democratic and egalitarian, while monarchy is not. Why is our head of state chosen by accident of birth? And, why can’t the head of state be someone born poor, or Catholic, or black or even Tasmanian?