Unlike in 4e, where there was no perceptible mechanical reason for the fighter to be restricted to 3 not-terribly-useful skills, the Fighter in 5e is going to be balanced across 'the pillars,' and is meant to be dominant in the 'combat' pillar, while skills figure prominently in the other two, thus, the fighter must be skill-poor.
The thing is, the fighter never has been allowed, and likely never will be allowed, to be as dominant in the combat pillar as other classes are allowed to be in other pillars. They're not even allowed to be as relatively effective in the other pillars as other classes get to be in combat.
Fighters get a
marginally better attack bonus than other classes. They get an edge in damage over most
if they choose to use their expertise dice in the least interesting way, otherwise they have no particular edge in damage. They
might have the best AC in the party, though there's certainly no guarantee there: clerics of the War domain have the same armour proficiencies, and a high dexterity character wearing light armour can match the AC of a heavy armour wearer. If they do have the best AC in the party, it's likely not by a large margin. With Fort/Ref/Will gone, and ability saves in their place, the fighter has no chance for any particular edge there.
A handful of theoretically possible marginal edges do not add up to dominance of a pillar.
I will grant that the fighter is currently the toughest of the classes, with the highest HP per level and the Parry ability granting the potential for once-per-round damage reduction. All else being equal, they'll survive the longest, which I guess is something. Not sure it's dominance, though.
Rogues
cannot fail DC 16 checks in skills they're trained in, and DC 13 checks in skills they're not trained in. Fighters can fail a DC 9 check that uses their best stat and a trained skill. In combat, fighters only have a +1 to-hit advantage over a rogue with a similar attack stat (+2 at level 4, before dropping back to +1 at level 5). Fighter's don't get some minimum attack-roll guarantee, nor a bonus that they can opt to use in place of their stat bonus.
Every class participates in combat. Every class gets combat-based features.
Every class should participate in exploration. Therefore every class should get exploration based features.
Every class should participate in interaction. Therefore every class should get interaction based features.