That's not the best way to word it. Mechanics and concepts map to one another. Adding mechanical options usually just changes some of the mappings (but not always).
The 'mapping' part is and always has been flexible. There is no 'One True Map' for 'strongest = fighter'.
So you can keep the concept of strongest and hardest to physically kill. It's just that concept maps to a barbarian now.
No, now that you have the option of fighter OR barbarian, you can choose
either for your 'strongest in the party' concept.
Likewise you have eliminated the concept of strongest and hardest to physically kill from the fighter class due to it's mechanics no longer respresenting that in the game world.
The barbarian is 'hard to kill' (concept) in a specific way (hit points, damage reduction), but you can have the same
concept using a different class (druid has many bags of hit points, fighters can have hit points AND full plate, Second Wind, re-roll failed saves, etc.).
So the new and interesting mechanics with the barbarian class do
not have the result of lowering the number of concepts the fighter class mapped to.
(Yes I know I've slightly changed definition of concept in this elaboration as I didn't really have a better word. Concept definition 1 = class and identity intertwined. Concept definition 2 = identity apart from class.)
Exactly!
Your house it built on shifting sand.
Let's go back to your concept: 'strongest'. Strongest what? Strongest PC in the party? That's not a character concept, that's something you might notice if you look at the character sheets of every PC and see which has the highest strength score. Even in OD&D there may have been two or more fighters. All it takes is four or more players playing a game with only three character classes, and any 'concept' of being the best 'X' in the party is no longer under your control.
Do you mean 'my class means I'm used to being the strongest in any group I belong to'? So all fighters and all barbarians are always the strongest in their group, and have grown so used to this that it is integral to their self image? How? That fighter, given the training rules in early editions, would have been trained from childhood by an adult fighter in a group of other children who all want to be fighters when they grow up. How can it be true for ALL of them that 'strongest in the group' is an inalienable part of their identity?
How can a barbarian, even if we conflate the game mechanics of class with the in world culture, have grown up with the idea that they are the 'strongest in the group'? He was raised in a culture where every single member of his tribe was stronger than every other member? That is literally absurd.
When these various 1st level PCs meet in their first tavern before their very first adventure, they cannot
previously have had 'I'm the strongest in my group' as part of their identity, and that cannot claim to be 'strongest in the group' before they know the strength scores of the other PCs.
It's really not a valid 'concept' at all! 'Strong' is a valid concept that you can certainly choose, but 'strongest' is not under your control because you are not in control of the strength scores of the other PCs.
'Strongest' was never a valid concept, so the appearance of another Str-based class cannot take away something that never existed in the first place.