The grizzled NCO (who can't make a fear save)
The officer (who is a poor leader compared to the court musician)
The noble knight (who is tongue tied next to the cut-purse)
The seasoned mercenary (who is a poor judge of men next to the Druid)
The sentry (who has weaker perception skills than a commoner)
In a sense, it is like phased in incompetence. A fighter will be hopeless at level appropriate challenges compared to the classes with a focus here.
"Can't"? "Hopeless"? First you are way overstating the case here.
Just comparing classes straight up the fear save is only 4 points behind any other class at 10th level through 13th level. "Can't" is not remotely accurate.
One feat, which the fighter has plenty of, and you erase half the difference right there. And if you design a grizzled NCO (defined in this case by ability to resist fear) with an 8 WIS, then you are not making an effort to design what you claim. So the disadvantage is quite minor and quite acceptable. The claim of "can't" is either poorly considered or disingenuous.
(As an aside, the fighter in Pathfinder gets a bonus specifically to fear saves that keeps them at or just -1 behind a good will save at every level)
When you talk about skills you are apparently presuming a generic build fighter and then declaring him poor at given specialties. You can easily build these options. Certainly I've always found it common that gaining a class skill is easy. But even without that an appropriate character build for the concept and simply taking skill focus goes a long way. Depending on how you build it, there may be no difference, or the pure fighter may lag slightly. But, again, "incompetence" is either an incredibly poor choice of words, or is not an honest presentation.
But then we get to the real issue, because all this above is just playing with a deck stacked in your favor.
Now you could multi-class in Bard or Rogue. Few fantasy characters can actually be modeled without doing this and still have them as capable as they are.
The system was designed with multi classing and prestige classes from the start. The presumption that these tools are there to complete a concept is a core element of the game. So taking that away isn't a quality assessment of the system.
I'd quibble over the bard because there is plenty of merit in avoiding any magic in a lot of concepts, and even if we assume you can simply reskin the abilities of a couple levels of bard, that is still a whole separate discussion.
But there is nothing whatsoever wrong in taking a few levels of rogue or barbarian or ranger or, of course, a PClass. It is assumed.
The fighter fights. That is what he does.
Frankly, if you just want to say that a Fighter16/Rogue4 is a better character than a Fighter20, you could quite possibly find me in agreement with you. But the pure fighter does put all his eggs in the "I fight" basket. And at very high levels you can also say that feats get a diminishing return.
But that doesn't hold nearly as true at 8/2 and 10. Not that there is anything wrong with a F8/R2, but the F10 works just fine and can be designed with a variety of concepts in mind, all before you get into the presumed idea of multiclassing and PClasses.
But when you say "can't", "tongue-tied", "hopeless", "incompetent", then you are way off base.