Sigh, let's go again. He said that the fighter can't contribute in a social or exploration pillars, NOT that the fighter isn't the best at those pillars. Yes, fighters aren't "da best" in those pillars, barring Athletics*, which is a darn useful skill for exploration, and tied to Strength, and Stealth, for Dexterity fighters.It's simple. Virtually nothing about the fighter class contributes to social or exploration pillars. It's unlikely that the fighter will have the Int or Wis scores to make him very useful at exploration, and, heavy armor means that most of his useful skills will be done at disadvantage. At least, he's useless at stealth at a minimum. Even with a reasonable Cha, his Intimidate likely isn't all that good either. Not compared to the other characters. Never minding that he has nothing to actually improve those checks - no Guidance spells, no Bardic stuff, and whatnot.
It's not that the fighter is bad at skills, it's that virtually every other class is as good or better. Same as the fighter generally actually. Sure, a fighter is effective at whatever schtick you want to give him, but, there's always another class that is as good at that schtick and most often better.
Just as a note, have you ever actually seen the Battlemaster "scan" ability used at the table? I haven't. Not once. AFAIC, it might as well not even exist.
But it is very different to say that they can't contribute effectively. Furthermore if you have in mind that fighters have better stats than average, so they can actually improve their average skills, without harming their battle prowess. Yes, he hasn't the Expertise of the rogues (although he could buy it with one of their free ASI, see Prodigy), but doesn't *suck*. Bards are great in SI, but they can't support their own efforts with Bardic Inspiration. Druids are broken, so I don't count them (actually they are my main beef against 5e, see above).
Also, did anyone ever played a fighter, really? You don't have disadvantage other than in Stealth, and you can always doff your armor and keep the breastplate. You'll have less AC (16 with a shield and no dex), but no disadvantage on Stealth if you need it. If you expect to fight, you could become the obvious threat, and grant advantage to your pals Stealth. And if you really need a stealthy party, cast Pass without trace and everyone in the party will have +10.
About the scan skill, I actually haven't seen a level 7 or above battlemaster. The fighters that I've DMed where Champions and Eldritch Knights (and they were far from useless in Exploration or social interaction -the champion Remarkable athlete feature is pretty great) But I'm playing a level 6 one, and I'm already demanding info of every important NPC, so I'm eager to have the scan. And I'm the skill monkey of the group (6 skills, 3 tools and languages, Expertise in Athletics, no multiclass needed)
*Athletics also involve: swim, climb, jump, and any prowess of strength (like rescuing a falling character, stop a massive boulder, breaking a barred door, etc). So, pretty useful.