First off...
One of the problems you run into asking questions on the internet is you really have no idea when you get answers who has the slightest clue what they're talking about.
Think of your printer as a piano, and think that anyone who tells you it doesn't need to be profiled as akin to someone who tells you your piano doesn't need to be tuned.
Yes, it's just that foolish. What comes out of the printer is not the truth. The color data in each pixel in each file you send to the printer is the truth. More truth is that whenever you send anything to a printer, some description of some printer condition made by somebody somewhere -- this description otherwise referred to as a profile -- is telling the printer exactly what dots to print. If the information in that profile does not match what your printer is actually doing, then you have to alter every single incoming pixel to try to match an unknown.
Somewhat akin to altering every note in every tune you play so as to try and make it be in tune on an out-of-tune piano.
So, though, all that said...
That's a very old printer you have there, and I've found all old HP's to be pretty unstable. And it is pretty pointless to profile an unstable printer, just as it would be to try and tune a piano that has -- say -- such a worn out pinboard that it won't stay in tune.
As cheap as newer and far superior printers are these days, I'd invest any money you might want to spend in profiling that old HP in getting a current generation machine.