While I agree a mounted, hardwired, onboard air compressor would be a fine thing to have, and really the only way to go for applications like air-actuated lockers and airbag helper springs, I find the portable 12v compressors with alligator clip power connections very handy both for off-road use and around the house. With a portable, you can deliver air to another vehicle without having to drive up next to it, use it in another application (blowing up floats at the lake or the beach), and most any other thing you can imagine.
I do strongly suspect you'll find a world of difference in beach driving once you get your pressure down below 20 psi. You need to be careful about hard turns and hard driving in general, as it gets easier and easier to pop a bead the lower you go on air pressure, but I've found that a light foot on the skinny pedal and common sense as to how I drive is 100% effective in not popping a bead. I have run the NC coast beaches for about 27 years in Chevy LUV pickup, Jeep Wagoneer, Ford F150, Isuzu Trooper, 2 different K1500 Suburbans, and now my F350. I've never stuck to where I couldn't self-rescue with a shovel and further pressure reduction, and never popped a bead.
Foy