Because a vast amount of drivers and riders never give their tyre pressures a second thought, they never think about the overall effects and consequences of failing to run their tyres at the correct pressures.
First off, the vehicle will handle, grip and brake better, whilst giving improved gas mileage (compared to running on under/over inflated tyres).
Tyres not inflated to their correct pressure can overheat and/or be subjected to premature damage and wear which may lead to sudden failure and the potential for loss of vehicle control. Extreme stresses on tyre sidewalls and the inability of the tread to grip road surface or to clear surface water/mud/slush occur.
It is standard practice for Police and other investigators (such as those employed by insurance companies and lawyers) to carry out vehicle inspections when accidents occur and claims are filed.
In the event that the tyres are found to be outside of the specified pressures, the driver may face charges for driving a vehicle in a dangerous condition and the insurance company can void the policy and decline payment for the same reason!
If incorrect tyre pressures are found to have contributed to, or been the cause of a vehicle crash/personal injury, the driver may face serious criminal charges and civil claims.
Personally checking the tyre pressures on your vehicle also provides the opportunity to visually inspect the tread and sidewalls for wear/damage/bulging etc.
When I ran my own motorcycle workshop, every bike that came in had low tyre pressures, some were run so low that they destroyed the tyres and inner tubes. Had I not seen this on a daily basis, I'd never have believed it!
Unfortunately, everyone I ask (when they last checked their tyre pressures) can't actually recall, some say that they leave it to the garage to do as part of the service schedule, or for the MOT test (an annual inspection on vehicles over 3 years old).
Bearing in mind that your tyres are the only contact your vehicle has with the road surface, I think they merit greater respect, and given that they carry you and your loved ones around, so should you...