Basically the benefit of airing down is increased foot print. All the other things like improved ride and less puntures are a bonus. The bigger the footprint the more traction, generally. Basically your ground pressure is the same as your tyre pressure. As with all things there is a trade off. Lower tyre pressure means less ground clearance. If you are running tubeless anything less than about 20psi will start to jam stuff between the bead and the rim (or even push them off the rim), although on clean sand this shouldn't be a problem. I ended up having to clean beads three times one weekend after running pine forest tracks at 20psi, great traction though. Depending on how stiff the side walls are depends on how low you have to go to get a good footprint. Some of my mates run Simex extreme trekkers and they have to go down to under 15psi to get appreciable sidewall bulge (and regularly run at 4-6psi with beadlocks), where I, with Mongrels from Motorway Tyres (these are simex copy retreads with tubes in) only have to go down to 20psi to get the same bulge and hence same footprint. If you air down so you have a lot of tyrewall bulge you run the risk of putting something through the sidewall. This usually stuffs the tyre, were as something through the tread can sometimes be repaired.
It is interesting to note the recommended pressure for a 2002 Rodeo is 26psi. That is only a few psi more than I used to run my tubeless Cooper STs at off road on my first gen Wizard (Rodeo). These are now my road tyres that I run at 38psi. If the stock shocks are crappy put some OMEs in. Finally on sand less tread is better, ie an AT is better than a MT which is better than a Simex type tyre, as they tend to dig in less.
