Is it just me, or has nobody has said a single thing the Fighter can't do outside of combat?
Exploration? The Fighter has high strength and proficiency with Athletics. The Fighter can climb up the cliffside, down into the ravine, jump across the pit, break down the door, clear the rubble from the cave better than anyone but an out-of-combat raging Barbarian, or the rare Strength-focused Rogue or Bard with Expertise in Athletics.
Not true. Anyone with a high Strength and proficiency can be just as good as the fighter at Athletics related tasks. I have played in a game where the Wizard had an 18 Strength, which was higher than my 16 strength fighter, so the wizard was actually better at athletics related tasks. The fighter has nothing that is class specific that contributes to completing athletics related tasks.
On the other hand, many classes gain features or abilities that allow them to outright bypass athletics related challenges. Shapeshifting druids can get more Strength than a fighter, a climb speed, or flight, all without using a spell slot. A valor bard with expertise in Athletics will generally have a higher Athletics check than your typical fighter. A spellcaster who chooses to use a low level slot on something like spider climb, jump, levitate, or misty step can outright bypass the same obstacles that your typical fighter has a 25-50% chance of failing.
Sure, the Rogue can pick the lock, but if he should fail and breaks the lock, you need the Fighter with a crowbar to crack it open. Yes, the Wizard could fly across the chasm, but why use a spell for that when the Fighter can just jump over it with a running start?
This is also untrue. In fact, due to bounded accuracy, anyone can accomplish a DC 20 Strength check if they have a 10 or higher strength. It is exceedingly rare that you are face DC 25 Strength checks. And even then, if the party has anyone who can cast the guidance cantrip and someone with a 14 Strength, it still becomes doable.
Also, what happens when you have a 30 foot chasm you need to cross or a 100 ft wall with a 20 DC. The fighter can't jump that far. And there is a very high likelihood the fighter would fall half way up the wall. But a spellcaster could use a low level slot and automatically pass such challenges with no chance of failure. Aka, when the task is really important, the one who is supposedly best at overcoming physical challenges has to play second fiddle to the casters.
Social interaction? The Fighter is no worse at social interaction than the Wizard, Cleric, Ranger, Monk, or Barbarian just at its base level. But give him a decent Charisma score and a background with a social skill or two, and you've got yourself a smooth-talking fighter. And don't forget that the Fighter gets the most Feats and Stat Increases of anyone. Make your Fighter a Face. Why not?
A few issues here as well. Sure a fighter with a 14 charisma and proficiency in charisma based skills is just as good at social interactions as a number of other classes...when those classes don't devote any of their spells or other class features toward being good at social interactions. A druid or ranger can speak with animals and gain information a fighter never could. A warlock can use one of his 8 invocations to gain proficiency with Persuasion and Deception. A wizard or cleric can utilize charm person, suggestion, or even domination to overcome social encounters. The fighter is stuck with only using his background and proficiency, which everyone also gets. Oh, and lets not forget that the fighter gains very little from charisma compared to classes like the Bard, Sorcerer, Rogue (Swashbuckler), Paladin, and Warlock. That means those classes are far better suited to being the party face as charisma gives them more than just a small boost to charisma based checks.
As to having more feats, well yes the fighter does have more feats. 1 more at level 6 and 2 more at level 14. Compare a level 10 fighter to a level 10 warlock, paladin, bard, wizard, cleric, druid, or rogue. That 1 bonus feat the fighter has cannot compete with the non-combat capabilities of those classes. For example, just from invocations a warlock can disguise self at-will, cast jump at-will, and gain proficiency in both Deception and Persuasion. Also, many non-combat feats are far more situational and far less useful than class features like expertise, reliable talent, or spells.
So what's the problem? Am I missing something?
You seem to be missing a lot. Sure, a fighter is just capable outside of combat, but they are the least capable class in the game outside of combat. Every class gains significantly more features that can benefit their utility outside of combat. Fighters don't. Sure, some class has to be the lowest rung on the ladder in terms of non-combat utility, and that class is the fighter (especially STR based fighters).
Some people wish that there would be times where having a fighter around would cause the party to go, "woah, I'm glad we have a fighter to help us overcome this (non combat encounter)". Instead of saying, "oh well, we don't have a fighter, but bob the 15 Str cleric with the guidance cantrip can do everything he could and more for noncombat encounters without ever using a spell slot."