Actually it should help with both, because a on-island terminal would also provide LNG storage capacity which would buffer short-term price fluctuations. We have zero such storage.
Again, our poor decision making around national infrastructure is on our governments. They left have left us completely exposed to international markets.
A lot of it relates to the planning process, they do keep trying to build things. One could argue that this is also their fault (and I do!) but there are good historical reasons (cough ray burke cough michael lowry) why we've ended up with such a bureaucratic, byzantine planning process.