Fighters do not need abilities or options other classes do not have in order to contribute outside of combat. The fact that other classes can also use the same techniques in no way affects the use of those same techniques by a fighter.
They don't need anything outside of combat that makes them uniquely capable in order to contribute. All PCs can contribute, regardless of class, outside of combat even if they are not the best theoretically possible.
If the party has to convince a guard to give them information and the bard has a +10 Persuasion and the fighter has a +3 Intimidation, they party will likely choose for have the bard rolls.
There are no official rules that incentivise the Intimidating over Persuasion.
There are no official guidance that incentivise the Intimidating over Persuasion.
Using multiple roles a complex skill system or skill challenges is not a coral of 5th edition either.
This is because 5th edition was written in a very simplistic manner with little margin of design choice and little respect to the idea that the DM might not have the answer or ability to balance it according to the makeup of the party.
Now if you're saying that every party member should allow the fighter player to choose their skills first and then ban any other player from using those skills or picking those skills as proficiencies so that the fighter player will always be the choice for using those positions.... well that's not in the game add rules guidelines nor advice
Now you can say it's not nice to pick the same skills as the fighter and then be stronger than them in the chosen area that they picked but 5E doesn't have a expensive skill system in the first place so there really isn't that many choices to pick in the first place. And once you pick your two skills from class and two skills from background chances are there going to be a ton of overlap which is kind of the whole problem.
There are
only 18 skills in 5E and every class has a minimum of four proficiency slots. And a couple's classes have get more than 2 skills. And racist gift skills. And some classes get skills.
So it's very very very easy for a fighter to be in an overlap but one of their party members if the group is four people or more. And Kord help you if you got five or more PCs in a group.
A dwarf fighter could easily be outmatched in Intimidation or History in the classic group with a human cleric, a halfling road, and an elf wizard. Add the tiefling warlock, half orc barbarian, half elf bard, or the dragonborn paladin and it gets really rough..
Wizards of the Coast made 5e a
little bit too simplistic and too small to match the style of game they actually want to represent as core. They created the rim of the crab bucket.
I think the playtest in 2013 Focused too hard on a very combat heavy module and didn't really get the non-comment mechanics right because they weren't tested enough.