Say an MP is a dual citizen and then they make a law that deals with trade with that foreign nation, or works directly with our intelligence service etc. There's no way to ensure there isn't a conflict of interest there. If their only citizenship is Australian, they can't make a dodgy deal and then go fuck off in the other country and reap the rewards.
Australia's Head of State is only a de jure Australian who rarely sets foot in the place. Are there any Jewish MPs in Australia? Anyone who is Jewish has an automatic and irrevocable right to take up Israeli citizenship, and Israel does not extradite its citizens. Has this provision of Australian law requiring MPs to not have any foreign citizenships ever been challenged in court?
A bunch of countries have the principle of jus sanguinis (right of blood) as part of their nationality laws, meaning that someone born to a parent from certain countries could choose to take up the citizenship of their parent later in life if they so chose.