Tire pressure is still important for Beach Wheels on differing surfaces. Same as for use on a 4x4 in sand or on the road.

On the extreme end of hard tires... the plastic Tiger Trax.

These are horrible in soft sand and rough surfaces, but great for hard sand and surfaces.

So... softer is still better in soft sand, but even the Cat Trax rubber wheel, when pumped up, is softer than the Tiger Trax wheel.