The way I look at it is, the tyre's main job is to keep the rim off the ground. The more air, generally the higher off the ground the rim. BUT also, the more air, the less give in the tyre sidewall, and therefore more vibration from our not so smooth roads gets transferred to other parts of the vehicle, notably shockers, springs, and chassis and occupants.
If your requirement is to save a few bucks on fuel & bugger the suspension, then pump up.
Interestingly, a fellow over on LCOOL as a big-wig with Cooper Tyres in Australia. I seem to recal a post of his complementing another bloke & his tyre fitter for NOT slavishly going for 40 psi all round but adhering to Cooper's recommended pressure for the particular tyre, which was in the low to mid 30s I think.