PSI devices

I remember in the Rocky movies the russian boxer was hitting this machine and it was measuring the pounds per square inch, the force of his punches. That thing looked really cool, and I wonder, at what point do people worry about that stuff? Does it not matter until you've developed a base of strength from pushups and the proper technique to accelerate properly?

The only time I worry about PSI is when I'm putting air in my tires.
In regards to hitting power, how the impact feels on the bag or the mitts along with the sound of the impact and how much the bag moves from the impact are all the tools I've needed to gage if I'm hitting hard enough.