No it's not. With 2 extra feats/ ASI and several Maneuvers (now available to all Fighters via Superior Technique) buffing skill use, there is literally nothing stopping a Fighter being top tier in Social and Exploration aside from the player making different choices (which is also fine).
LOL. First "superior technique" into skills gives up a
lot of combat power. Second it's effectively equivalent to expertise but can only be used once per short rest. That said there's some cute synergy you're showing between Superior Technique, Martial Adept, and the Great Weapon Master feat because (as with spell slots) you can spend it both into and out of combat in different ways. But you
need the feat for that.
Lets look at one of the Weakest Fighter subs, a Banneret at 13th level. Noble Background. Vuman (Str/ Cha).
I think there's some cherry picking going on here; Banneret for the free expertise, Vuman to be able to take an extra fighter feat and 13th level for the +5 proficiency here.
In addition to GWM (Human), he also Buffs Strength by +2 (4th), takes Skill expert (Insight, +1 Strength) at 6th, and Martial Adept (8th) and +1 Str/ Cha at 12th.
So let's look at that build. In specific from levels 1-5 you are a standard "commoner" fighter - and even behind your average fighter because you've chosen to put what would often be racial background abilities into Great Weapon Master. (That's assuming you've started with Precision Strike from your fighting style; without it you're likely to not get that much mileage out of GWM).
Your social abilities come on line at levels 6, 7, and 8.
But. (And there's always a but). Because you chose Skill Expert at 6 and Martial Adept at 8 your STR moved to a +4 bonus (alongside most fighters) at level 4 and only moved to +5 at level
12. You've an exceptionally soggy tier 2 combat growth there to the point that the only meaningful differences between your fighter in combat at level 5 and level 9 is a lot of hit points, +1 proficiency bonus, a single use per day of indomitable, and a battlemaster dice.
So playing through this build is going to feel bad. Levels 1-5 you're a commoner out of combat and levels 6-9 (6-10 in the wrong party) you gain almost nothing
in combat.
Skills
History +5 (+1d6)
Persuasion +13 (+1d6)
Perception +5
Insight + 10 (+1d6)
Athletics + 10
Intimidate +5 +(1d6)
And having burned all that you're still bottom tier in exploration and your numbers in the social tier are not
nothing. But all they are is bonuses on a d20, leaving you fundamentally unable to change the situation. Yes, those are some nice numbers - but you're mid-tier at best.
Essentially all you are out of combat is effectively the player of a commoner with loaded dice. It doesn't allow you to do anything anyone else can't - just gives you a good chance of success.
Fluffy (a Noble Knight archetype) who runs rings around even the Bard in the social pillar,
Lol, nope. A
baseline bard at that level should have a Persuasion of +10. Give the bard the Enhance Ability spell (a good general buff that doesn't have to be used socially) as a second level spell and it's in striking distance of your Persuasion thanks to Advantage. Add in an illusion spell (I don't care which one) and the bard is running rings round you. The only bards you're actually running rings round are those that have spent precisely no spells supporting their social abilities.
and can jump, climb and swim better than anyone else in the party.
That and two dollars will get you a coffee. Flight's been online since level 5. Water walk and water breathing have been
rituals since level 5. And it's not hard to get a swim speed (or for that matter a climb speed) - which will leave your ability to swim almost floating idly.
He's also a GWM Fighter, with Strength 20 and Precise strike to land them.
And as pointed out getting there was a chore for him.