You raise a good point that balance must be examined at the party level.
Maybe a better way to describe the issue is that wizards have greater versatility of class options than fighters. So, a wizard can be built toward combat, exploration, roleplaying, or some balance of those things. A warrior, OTOH, is squarely focused on combat (and has few options for expanding into other dimensions of play). Now I've had the pleasure of playing with some really great players of warrior PCs who brought a lot to the table outside of combat, but that was always by virtue of their own roleplaying skill in spite of the rules.
What I believe the argument for more versatile fighters is about is taking some of the more nebulous aspects of fighter that succeed or fail at the DM's whim (which can be good or bad, depending on the DM), and giving those expression in the rules. Doing so also could be seen as an imagination tool to inspire fighter players...just as spell descriptions can inspire wizard players.
You might not agree, but what I've just described is an entirely legitimate position.
It's not saying D&D 5e is broken unbalanced, it's just saying there's room for improvement. Much in the way that Inspiration has been well received as codifying in the rules something that was happening at many tables anyhow.
I think that WotC has already added in that improvement. The more versatile fighters are already here.
A player wants to be a melee PC and cast spells? Then take Eldritch Knight, or Arcane Trickster, or multiclass into any type of spellcaster, or take Paladin, or Ranger, or Bard. A player can still get in 4 attacks per round and still cast spells.
The options are already there. I do think that some players want to have their cake and eat it too. Or they want to "stay away from magic", but still do magical type things.
Yes, wizards have greater versatility of class options than fighters, especially at higher levels, but then again, fighters now have many of those same versatility of class options, but at much lower levels.
In 5E, it's up to the player to decide if he wants to play a fighter with those options, or if he wants to focus more on melee combat.
Still not seeing an issue here.
And I also do not see a need to make high level supernatural fighters that can jump from mountain top to mountain top without using spells, cleave a boulder with their bare hands without using spells, or stem the tide of a raging river without using spells. That tends to be the exception in fantasy fiction instead of the rule, regardless of players wanting their fighters to be able to do these types of things.
I get it that some players want fighters to do supernatural things, I'm just not one of those people. I think that PCs have roles and niches in parties and the designers should not go out of their way too much to blur them. The designers should put the brakes on some of these more fantastical martial notions. IMO. This blurring is not needed because the party does not need that. The party needs skill monkeys for non-combat situations, and spell casters, and ranged combatants, and melee combatants. Yes, the spell casters can cover many of those roles, but that's THEIR niche. WotC is already giving a goodly portion of the spellcasters niche to the martial types, yet some people clamor for more.
