That is a great observation about the sand. Once the roots grow in, the sand should be stable even when dry. That has been my observation with sand. I have even used coarse kitty litter. That stuff is unstable wet or dry until the roots grow in. After that it becomes very firm.

Yes the sand incorporates in time with both the existing soil & the roots & thatch of the lawn. The situation I am referring to has water coming up & through from beneath & other sands won't do the job, it has to be this unique coastal sand or sand with the same qualities. If one wets building or normal quarry sand it goes sloppy & then hardens on drying. . . . . . the opposite reaction to the beach sand. I found this by accident when a load of the pit sand washed down in a storm to an area of low-lying lawn which had always always been seasonally boggy . After the pit sand had covered the area & the grass grew back the whole area was firm & stable all year round!

That has been a long held practice with golf courses. It is also very commonly used on parks in my area.

Well there you go, all my life I've made great discoveries only to find my revelation had come somewhat late. I once when young, had a bright idea for a perpetual motion machine & when I ran it by a technically minded friend he said a little wryly "yep you've just described an electric motor"

Having or using the discovery and sharing it are two (three?) different things. Another Aussie came here a few years ago to reveal his method for chopping very expensive bermuda sports sod into pieces and spreading those onto his prepared soil. He had a full bermuda lawn in 6 weeks. It turns out golf courses have been doing that for years, but not in the economical way that he came up with.