This complaint makes no sense - it's like complaining that a rogue out-damages a fighter with sneak attacks even if the fighter is the sneakiest attacker on the planet!
Which is a perfectly sensible complaint! After all, one of the biggest problems with the 2e rthief. Why can he hide in shadows and no one else can access this special rule (excepting a few niche classes with access to thief skills)? What happens when someone else tries to be stealthy?
Of course, this was neatly solved with the 3e rogue by moving it to the skill system. Hiding is now independent of class, and the rogue simply receives faster advancement in it. Looking at the rogue class tells you nothing about how hiding works, only about how good the rogue character is at doing it.
Of course, you're right that the new issue is why the rogue seems to be the only character that seems to gain any real advantage from stabbing someone in the back. The solution is the same: write complete combat rules independent of any class that describe all possible actions and scenarios, and make the character creation rules simply describe who is incrementally better at backstabbing (or swinging hard and recklessly, or using shields, or channeling rage, etc. etc.). Reading the fighter description should tell me absolutely nothing about what actions can be attempted in combat or how they work.
The continued presence of endless menus of specialized, exclusive class abilities is a far bigger issue than any one particularly poorly designed ability.
That's what a D&D-style class system does.
That is sometimes what the anachronistic aspects of the D&D class system do. Exclusivity has disappeared over time. It used to be that a D&D-style class system meant that you had to pick what class you were from the start and could never change, or that what race you were tightly restricted what classes were available to you. It's perfectly natural to continue removing restrictions that are unneeded or which don't make sense.
It's a class ability that some players choose. Nothing in the rules indicates that that player choice corresponds to any sort of character choice.
Another one of the beauties of the 3e skill system, which explicitly states that characters know what skills they have and choose to train them. Of course, I can't quote any 5e text, but I think it was pretty clear that character classes are not metagame constructs. Certainly, a "D&D-style class system" in general refers to a set of in-game choices. Fighter are aware that they are fighters and not wizards, and they know why. I don't think it's a big leap to say the same of the consequences of being a fighter (class abilities).