And the fighters aren't casters at all. The PHB doesn't say it's bad to not be a caster.
Agree, but stating that the Wizard is the supreme caster means explicitly that all classes are not balanced. Specifically - Bard, Cleric, Druid, Ranger, Artificer, Warlock and Paladin are all casters and the Wizard is superior to them.
Now you can argue that it does not say explicitly in the text descriptions that Wizards are superior to Fighters, Barbarians and Rogues, but your statement was "all" characters are balanced according to explicit and implicit claims and in actuality the explicit text in the Wizard class is that they are supreme among 8 of the classes and therefore it is explicit that not all characters are balanced.
At best your argument is Rogues, Barbarians and Fighters are implicitly balanced with Wizards, while the others aren't, but I don't know of any text that actually implies this anywhere in the PHB.
Finally playing a weak class does not mean that it is "bad" to be that class. You should play what is fun for you, whatever you want to play, with a group that is willing to accept that decision.
The reason the PHB does not say
"it is bad to play a fighter" because it is not bad to play a fighter and I am not stating that it is bad to play one, or any class if you want to. You should play what you want to play with a group willing to accept that decision.
Personally, I don't play Barbarians or Druids at all and I very rarely play Bards. That doesn't make those classes "bad" to play and in fact Druid and Bard are both more powerful than Monks and Fighters which I play often.
The idea that a wizard of level 17 should be more powerful than a fighter is not something that is made explicit or something that should happen.
It absolutely is made explicit when you consider the spells and class abilities. These are explicit rules.
The Wizard class has mechanics written in the PHB that state he gets to learn 2 9th level spells at 17th level, those two spells can include Wish, and the spell table shows that he can cast a 9th level spell once a day .... in addition to all the other spells and the copy he can make of himself with a lower level spell!
The PHB explicity states that Wizards get those powers. The PHB does not offer anything remotely comparable for a fighter. That alone explicitly shows a Wizard is more powerful than a fighter.
It is right there in the PHB. It is the explicit and undeniable promise made by the rules themselves - Wizards are more powerful than fighters at 17th level.
How could you interpret the mechanics any other way?
..... that do not deliver on what is promised by either the rules or the fantasy of playing a fighter. This needs fixing.
Where is this promise? Provide a reference in the game rules please. I gave two explicit examples above where the opposite is actually stated or shown.
It does not need fixing at all, it needs to stay unbalanced. Balance sucks the life out of the game IME.
So you think CR is not a thing? Because there is no adjustment to CR or to the level of an adventure based on party composition that I have ever read. Which there would be if it was intended that wizards were the best and fighters were meant to be bad.
I think party composition is huge and to think it isn't is to suggest there is no value in diversity. The CR tables are an estimate based on an average party which includes a mix of both "strong" and "weak" classes as well as strong and weak builds among those classes. Regardless of individual class strength, a diverse party will generally fare better than a non-diverse party even when class strength is taken into account.
If this myth about CR indicating class balance were true any party of a certain level should fare the exact same against every monster of the same CR. So whether the party is a diverse mix or classes or it is a party made up only of Monks or a party made up only of Rogues or a party made up only of Wizards - if you believe what you CR implys equality then all four of these examples should do just as well if they are all of the same level.
Further, experienced players operating with good teamwork will generally destroy those CR tables beating deadly encounters with relative ease, even while playing "weak" classes or "weak" builds. Meanwhile inexperienced players or even experienced partys that are not coordinated and do not leverage the particular party strengths will get slaughtered in those same encounters. That is far more important than the builds or the classes themselves.
If there is an implicit promise that the game falls short on delivering it is that "deadly encounters" or "easy encounters" are actually deadly or easy at those levels.
Finally, if we are comparing fighters and wizards - a party made entirely of fighters will actually fare better in some encounters than a party made entirely of wizards against certain enemies. Not many but some.