I've always disagreed with the notion that the martial classes can't engage with the social pillar of the game...
Also IME, the character that ends up doing the most in the interaction pillar is often the one played by the player that actively engages in it...I will admit that YMMV on this though, it requires a DM that is on the same page as you.
		
		
	 
True.  In classic D&D, where there was very little to the resolution mechanics in said pillar (typically just a reaction adj that got the ball rolling), CHA was very much a dump stat for that reason.  It had little mechanical effect, and the one place it should matter, it didn't, only the ability of the player to persuade the DM mattered.  
You could argue that we're back to that, with so much responsibility for resolution, balance, &c on the DM's shoulders, but, I think, as DM-dependent as the check system is, it gives CHA enough visibility that the DM will be reminded to keep that stat in mind.
	
		
	
	
		
		
			But really, between the "fighters suck" threads and the "fighters are too OP" threads, I guess that just proves they did it right.
		
		
	 
 It shows the fighter's been balanced in a very extreme way.  It's given high DPR via a mechanic - multiple attacks/round - that has proven problematic every time it's been implemented, even in the most carefully-balanced versions of the game, making it potentially broken in combat.  (Excessively high DPR isn't a benign kind of broken, either, it makes combats short and boring, and pushes the DM into an arms race to try to make the one round his baddest monster gets to act have an impact.  The fighter may not be there yet, as a matter of course, but every bonus that can be applied to all attacks in a round potentially pushes him in that direction.)  
Then, they 'balance' the fighter by giving him virtually nothing else.  So you have a PC that is boring to his player for most of the the game, and also self-limits the pillar at which he actually shines, by reducing the time spent in that pillar, and rendering it boring for everyone else (but, really, that's a win, too, ass fast combat was a major 5e goal).  Now, that's still not just the fighter.  Other classes use equally poor balancing strategies - but few as clearly bad as the fighter's.  
You're hearing two valid complaints about the fighter, and they don't contradict eachother the way you think.  The fighter can be broken in terms of DPR pretty easily.  The wrong feat, the wrong magic weapon, and *boom* your Legendary BBEG campaign-capstone encounter is rolled over like it's nothing.  So the OP charge isn't baseless (though it's really unlikely to happen much, and it's fairly easy for an aware DM to head it off, ironically, by limiting or not using feats & items).  Similarly, the fighter is minimally-contributing everywhere else.  Interaction, Exploration, even aspects of combat other than single-target DPR, give the fighter little opportunity to contribute meaningfully (contribute, sure, but mostly warm-body contributions that anyone, even classless individuals could have done), and virtually none at all to shine.  So the 'SUX' charge is back, and not entirely without reason. Unlike the OP potential, the fighter /is/ likely to sux a lot.  Often because any player willing to settle for a fighter is aware of that classes long-time stereotype, and wanted to avoid participating in the other two pillars, anyway (that's why he brought that mobile device to the game), or because non-participation goes unnoticed as long as one or two players are actively engaged, or, when the DM is alert, concerned and talented enough, because the DM tailors his adventure to keep everyone involved, regardless of class.
The saving grace of 5e is that it Empower DMs to fix issues like these as they come up.  It's a sort of synergy of goals.  DM Empowerment and Classic  Feel were both clearly very important goals from the start, and, while classic feel requires that classes be imbalanced in familiar ways, DM Empowerment presents the tools to resolve those disparities within the context of the individual campaign.