As stated before, the sidewall number is the maximum allowable pressure
It is the maximum pressure for the load range. The bead seating pressure is the maximum allowable before the sidewall goes. The trick is that tire pressure is dynamic. You measure it at 60F at 1200ft with 25% humidity and it's *this*. Drive all your friends down to the beach at 90F and run over a speedbump too fast and it will be entirely different. If you stay on top of it, that might work. If you inflate it to the 44psi on the sidewall, you may find it dangerously close to blowing out when conditions change. The manufacturer has (with the notable exception of Ford) generally done the math (and hopefully testing) to give you a number that will not allow you to cross the minimum/maximum under normal conditions.
when you get your oil changed it's a good idea to tell them not to mess with your tire pressures
I always asked customers how far they had driven to get to me and only really made an effort to inflate an obviously low tire. If it was cool out and they had just driven around the block to get to me, I'd set it to the manufacturer's recommendation. After more than maybe 5 miles, or if it was a hot afternoon, you can't tell. On a warm afternoon, I could tell a customer what direction their car had been facing while parked by the tire pressures. You could have one side sitting at the specified 32# and the other side at 38# if they had parked it right.
I check mine in the morning while still in the garage, and I'll usually overinflate by less than 10%, but I do exceed the sticker pressure on most vehicles. Except Ford SUVs (which we called "flippers").
I did have a few come in with 12#. I don't know how a tire stays on the rim at that pressure, but they did. Also, it's all different with low-profile tires. They'll pick up the same heat from the road surface, but far less solar gain. They also have a lower volume, so their pressure drops faster.
If you really cared all that much, you'd run the tire over a wet paint stripe at varying pressures to find the largest contact patch that stayed on the tread. That's probably going to be the "best" inflation level. The thing is that there is no magic number. Overinflated tires have lower resistance so you'll improve your mileage. You'll be riding on a thin strip of rubber, so you'll lose handling and tread life. At current prices, halving your tread life might actually be worth it, but do that in the rain and you yourself might live half as long.
ETA: You will need a MAJOR change in tire size (like putting gigantic mud tires on your Jeep) to change the optimum pressure by more than the margin of error on your gauge. If you change the load range of the tire,
then you'll throw the pressure to something completely different.
