When they had ATSIC, it was abused and that is why it was taken away from them with bi-partisan support.
There is nothing stopping the Govt. implementing a legislated Voice.
The Uluru Statement, the protagonists involved and the expressed desire for truth, reparation and paying the rent is not necessarily benign.
Placing a Voice in the Constitution presents all manner of Sovereign-risk and the possibility that it will thwart efficient governance is fraught. The legal implications and the access it provides 'to use their (our) own laws against us' is a risk not worth taking. Remember we're on a share trading forum that's meant to assess risk.
The threat to Sovereignty is demonstrated by the views/intent of the Aboriginal-mafia driving it: 'Always was, always will be', 'we never ceded sovereignty' - and this from someone who has pledged allegiance to Oz. As for the Mayo character...