So simply put that the reason for finding the pressure height is to find the actual altitude of an aircraft?
No, you've missed the point here. Lets start at the beginning.
We use pressure to measure altitude, as pressure drops as you climb, typically at 27' per millibar of pressure difference.
Air pressure at the surface varies, both higher and lower, so obviously you need a starting point to refer from. That's why they came up with ISA, and the standard pressure, which is 1013 millibars at the surface.
When they then test aircraft, they calculate and write down how the aircraft will perform on an ISA day, and that is what you use when you calculate how it will perform in the actual conditions.
On any given day, if you set 1013 on your altimeter, that is your
pressure altitude. It has nothing to do with your actual altitude, that would be shown by setting the sea level pressure (QNH) on your sub-scale. Its is purely used in performance calculations, and when flying IFR we set 1013 and fly flight levels to aid aircraft separation as we're all flying on the same sub-scale.