> The coast-to-coast "long distance transmission" is not in fact a thing in Australia.
The main Australian electricity grid reaches from Cooktown in far northern QLD [0] through to the Lower Eyre peninsula in South Australia [1] and down to the Huon Valley in Southern Tasmania [2]. So if by "coast-to-coast" you mean "East Coast" to "South Coast", then literally we have it already.
Of course, I take it you actually mean including WA and NT into the main national grid. No, we don't have that, and probably won't any time soon.
But there is a project (Australia-Asia Power Link aka SunCable) [3] to run a HVDC cable from Central Australia to Singapore via Indonesia, to export solar power. Why not the same thing between Perth and Adelaide? It simply comes down to economics – Singapore and Indonesia have the energy demand to economically justify it, domestic Australian consumption doesn't.
However, there is a plan to extend the national grid to Mt Isa. [4] There's only around 600 km from Mt Isa to Tennant Creek (where the AAPL/SunCable project starts). It isn't impossible that they'll eventually link up. So we might actually see the northern NT connected to the national grid, eventually.
[0] https://www.aemo.com.au/-/media/files/electricity/nem/networ...
[1] https://www.aemo.com.au/-/media/files/electricity/nem/networ...
[2] https://www.aemo.com.au/-/media/files/electricity/nem/networ...
[3] https://en.wikipedia.org/wiki/Australia-Asia_Power_Link
[4] https://en.wikipedia.org/wiki/CopperString