I agree with that policy. Should I ever run for office, I would actively renounce my other citizenship(s). It wouldn't apply to Musk though, because his escapades are not as an elected official.
https://www.abc.net.au/news/107237782
But no, nothing to do with the constitution. The link is to a commentary from a recent Australian ambassador to the United States. He was also our Treasurer, from the conservative side.
The headline says: "US corruption allowed to flourish in Washington during Trump's second term", but thats click bait for the Australian's who dislike Trump (most of us). Hockey's concerns go well beyond the current adminstration:
> "There's just too much of a blurred line between the financial interests of various administrators, including the Congress and the private sector."