I was specifically referring to air-only mattresses, where the density is the same, regardless of it’s thickness. Quite simply: unlike fiberglass batt, down, or open celled foam, air does not get more dense inside a compressed pad.
The air *is* the insulation in fiberglass batt, down, or open-cell foam insulation. Air is a great insulator as long as you can keep it from moving, which is the job of the other materials. Increasing the density of, say, fiberglass fibers makes the batt do a better job of stifling convective currents in the air. There’s a limit, of course, beyond which further increasing the density causes conduction in the fibers themselves to short-circuit the air’s insulating ability.
Any air mattress with an R greater than about 1.0 has some fiberglass or other “stringy” insulation in it, and compressing that certainly does increase its density. How much that matters is the open question. I’d also like to know whether all the movement (for us rotisserie side sleepers) causes enough air movement inside the mattress to noticeably degrade the R.

