Sadly, Australian golf played day to day by the masses is much the same as the US. Overwatered, over treed and covered in spongy kikuyu. It is just the top end that gets it, or perhaps more exactly it is the top end that is able to get it in having the funds to maintain proper bermuda fairways and the land to allow width.
Australian golf is very metropolitan. Most of our courses, and indeed our great courses are in the cities themselves, rather than being out in the country side as is more common in the US and the UK. Most then are now quite constrained in terms of land and with the modern game they cant remove the trees as that is often all that keeps people from being killed by errant balls.
RM is a decent sized property, but is beautifully routed in order to extract as much playing space as they can. LK on the other hand is a massive property, and they can pretty much do whatever they want.
As far as mowing is concerned, yes there is no rough at LK, or at least none where most of us might end up. The first cut is only about 10-15mm, just enough to stop the balls running down the hills and make approaches a little trickier. There is no retic in the woods, but grass does grow with winter rains, but it is regularly slashed out, especially at the start of summer. It speeds up play by eliminating lost balls, opens up the sand for interesting lies, and reduces the risk from fire and snakes - the latter two are quite important when you have spectators wandering about the place.