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Forgive the slight rabbit trail but race cars might have between thirty and fifty PSI more or less depending on tires, down force and a world other parameters. It is a rule of thumb that for each pound of tire pressure it is equivalent of fifty pounds of spring rate. That's in tuning the suspension balance and changes the dynamics of the car. It's also why pressure balance is so important.
The difficulty is not so much keeping the pressure even side to side but what about front to back and it's effect on oversteer/understeer. Many factors such as static vehicle balance, spring rates, changing payload, etc determine handling characteristics. Tires slightly low and soft promotes good ride and tends to mush the vehicles handling making it docile to drive. Anybody who's played with tire pressures a bit knows how quickly things can change. Wet vs. dry handling etc. Snow is an area where hard tires make good skis. Wet as well can be an issue if inflation pressures are too high or too low. It's not one way or another and you couldn't possibly expect your local tire store to know how to balance your vehicle under all driving conditions and thus the rule of thumb tire pressures.
All I know is running in the forties makes the ride a little bit harsh, improves fuel economy, and stiffens up the cars responsiveness. On soft surfaces like sand and snow, softer makes the tires conform more and have a lot better traction. More pressure can be good until it is too much then it's very bad if traction is diminished too much. Too hard to facilitate low rolling resistance can be as bad as too skinny and loss of directional control. Baby steps. Each car is different.
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