The tyre flexes as it rotates under load, that makes all the parts move in relation to one another.
If you take a piece of plasticine and squeeze it into different shapes, it warms up because of internal friction.
A tyre does exactly the same. Low pressure = excessive distortion or flexing = heat build up = structural damage.
The damage may not be immediatley evident - layers of rubber becoming unstuck - delaminate. Wire in beads detaches itself.
These ‘little’ problems will weaken the tyre, and gradually spread as more journeys are made. Eventually failure will occur (blowout). The lower the pressure the sooner the failure. A defecit of 5-10llb/sqin will affect its lifespan.
Also as you know with the bike tyre pressure affects handling.
Tyres are not rigid and flex or give under forces generated by steering, cornering, side winds and road camber.
Under these forces the tyre will seldom run absolutley straight but will ‘run off’ to one side. This ‘run off’ is proportional to the side load applied, and will be greater if the tyre pressure is lower.
If the ammount of ‘run off’ is equal on all tyres around the vehicle, they all behave the same making the vehicle stable.
If the rear tyres are a bit soft, they’ll ‘run off’ more than the front ones consequently as you turn through a corner the back end will run wide, tightening the curve of the vehicles path. You have to back off the angle of the steering wheel to compensate.
The opposite happens if fronts are soft.
If you find that you are having to regularly back off the steering halfway through a bend, (or have to apply more) your tyres will probably benefit from pressure adjustment. 2lbs will make a difference
If anyone thinks that I’m being a bit too fussy try driving through the alps fully freighted. 
You can get digital tyre pressure gauges now I check them weekly.