I have driven my LR3 and LR4 a LOT on the sand for the past 14 years. I have to air down.
If I go out at 42/36 psi I get stuck in soft sand. If it's really soft, it happens almost immediately. I'm talking soft fine beach sand when it hasn't rained in a while...
...so, now I always air down. If I think the beach is pretty firm I'll go down to the low 22-24. If I just want to be safe side I'll drop them all to 19-20 and not worry about just about anything. If I get stuck, I drop them to 15-16, put it in 4Low and I can drive right out.
When I say "stuck" I can tell when the truck is digging itself down so I stop before I'm resting on my frame. Then I drop the pressure, make sure all 4 wheels have a clear path by removing sand from in front of them, put it in 4Low and ease out. Works every time. In 14 years I have only needed a beach pull out once.
When I first used to drop the air down I would worry about the tire rolling off the rim on the road when I went around turns. I mentioned it to my mechanic and he commented on how hard it is to break a bead on our wheels, and not to worry about it. So, now when I have a beach vacation, and I'm driving every day, I just drop the air down on the first day and leave it there for the week. I don't leave it below 20, and I'm not typically driving over 50mph on pavement, but have never had any issues related to tire wear or anything. I know driving around that low isn't recommended, but it takes a while to air down and air up if you do it every time you get on/off the sand, and I have not had any issues.
Once you have driven the truck on the sand a bit you'll start to get a feel for when it's working hard and when it's driving easy. When I can tell it's working more than it should, I drop the air further and the thing feels like a dune buggy floating along the tops. Very cool. 5,000 lbs on 19" rims. Amazing.
That's my take, anyway.