static and dynamic load, speed, pressure, temperature, traction, sidewall deformation, construction, road surface, gas, humidity, comfort, and no doubt a whole heap other variables. Load, speed and pressure are a useful, practical, pragmatic, approximation.
My materials background (I'm really a metallurgist with a lot of other experience) suggests that impact loading is more of an issue for brittle than ductile materials. Charpy or Izod test if interested.
Thinking about it my mental model of tyres suggests that I lower the pressure to gain traction on sand or mud surfaces. I lower it but not by as much for comfort on corrugations, and I raise it for prolonged high speed motorway driving for temperature and tyre life. Rock crawling I'm a bit mindful of the balance between traction, what may happen when the wheel drops off a rock, and uneven wheel loading, so tend to reduce pressure but not by as much as for sand..
But fundamentally, in my case my tyres (Toyos) are so overrated for my vehicle axle and wheel loading I have trouble keeping the pressures low enough to be comfortable. Restricted by poor (IMHO) regulation.