Two additional uses alongside engine braking controlling downhill descents:
Low gear, high revs uphill on loose ground like sand
If you need to go up a steep hill on loose terrain like a sandy dirty track, dune or fine gravel, you need to build up momentum before hitting the incline and you need to put your foot down and get high revs for the speed you're travelling at. Leaving an automatic on D risks it going up a gear too quickly, having insufficient power and losing momentum on encountering the incline leaving you in stuck with wheel spin. Fixing the gear in 1 or L lets you put your foot down and get the high revs necessary.
I lost a tire in a remote African village attempting a dusty sandy hill in D then losing momentum like this. After changing wheel with some help from the villagers, then rolling all the way down to flat ground, I hit it in L with foot firmly down and cruised over the hill like it wasn't there.
From Land Rover's off road driving guide:
Deep mud or sand needs a steady momentum to carry you through ... in sand, the lower gear the better.
Higher gear, low revs on ice and mud
Too much power when driving in icy conditions or wet mud will simply cause the wheels to slip, so you might want to put the gear in to 2nd and then drive with low revs. In D, it might drop down a gear and you'd have too much power.
From Land Rover again:
In mud, too low a gear causes wheel spin.
More from the BBC
Stay in a higher gear for better control, and if it is slippery, in a manual car move off in a higher gear, rather than just using first.
In very bad conditions, crawling along in 2nd (and possibly even starting in second, depending on how the particular automatic transmission adapts) might be necessary.