Just so. Unless your tires are very skinny and you are pretty heavy, you probably don't need that kind of pressure. Frank Berto's tire pressure chart is a useful tool for estimating the tire pressure you need. Not everyone agrees with the specifics, but the general principle seems pretty robust to me:
And if that gold-standard chart doesn't reach the tire widths you are interested in, you might give a try to
my attempt to capture the essence of the chart in a formula, to apply to any values of load/width.