On my machine and the Marlin it runs on, I run a auto tune with a cold extruder. It heats to the temp it needs and does it's thing and gives me an output I use as the input for M301. I save that with M500 and the hot end is tuned correctly to maintain a steady temperature no matter what it is set to. This M301 setting is tied to a hot end. I have 4 hot ends one with a different nozzle size each. I have all the PID setting stored in a spread sheet so I just enter the correct string when I switch hot ends. So you tune it once and you are done. If you notice the temp swinging a lot when printing, it may need to be retuned to compensate for heater ageing.
Hope that helps.

Example of one of my settings for one particular hot end M301 P19.93 I1.51 D65.71 That gets entered on the terminal and then M500 to save it.