It's a statement of focus, not one of balance. (That said, as mentioned, it causes problems with the sorcerer).
It is not, and the mechanics show you are wrong. They show that the Wizard is in fact not just the supreme caster, but the supreme class.
You can't interpret the context of that statement without considering the mechanics
I mean you are saying that it does not mean that the wizards are superior as a class, but the mechanics on the very next page show that they are.
This is the problem. The thing is the fighter should get something awesome in tier 3 and be awesome in tier 4.
No they shouldn't. The fighter should get no more buffs at all in my opinion.
Further this would not achieve balance, people say they want balance, but they don't want to do what would actually provide balance - give the Fighter spells and a full spell caster progression. That would actually balance the fighter with the caster classes (or do a lot better than it is now).
There is no good reason that tier 4 fighters shouldn't leap tall buildings in a single bound and be faster than a locomotive. They just don't - but if they did it would not do one single thing to interfere with wizards being supreme casters.
Spells are the answer here!
If you want them to do this give them spells and then they can cast fly or dimension door or whatever so they can leap tall buildings in a single bound.
If you are not willing to give fighters spells then there is no reason they should be able to do these things.
The fighter should not be running around doing things that a Wizard or Cleric or Druid can't do without casting spells. If the fighter can leap buildings without a spell than those other classes should be able to as well.
One of which you are misinterpreting, as I have shown. And the other one of which is a result of the mechanics being bad and it's being suggested should be fixed.
Where does it say they are broken?
You keep citing this explicit and implicit promise, but then can't provide a reference to such promise. You may not like the references I provided, but they are there.
I have already pointed out that CR is a thing - and works on character level but does not weight for class. And I have already pointed out that adventures are for set levels and do not weight for class. There is no guidance anywhere that says to the DM that you should balance for class.
There are so many problems with this theory:
1. It does not weight for party composition either, or build or experience level of the players. Does that mean D&D promises all those things are balanced? There is an implicit promise that a party of first time players is as poweful in game as a party of experienced players because of the CR tables?
It does even imply that all classes are balanced any more than it implys all players are balanced (and clearly they are not).
2. The CR tables in the DMG apply for groups of 3 to 5 players. This range itself implys your reasoning is wrong. If all classes are supposed to be equal then something that is medium for a 5-member party could not also be medium for a 3-member party that has 40% fewer actions every turn. The CR tables are a guideline for
3. it does actually talk about this in the DMG about tailoring specific encounters to party composition, noting that Rakashas are immune to spells below 6th level and that you need to consider things like that as they could make an encounter more difficult for a specific party than another monster of the same CR. It also talks about modifying it for circumstances, specific "benefits" or "drawbacks". Those things would logicially include class-specific benefits or limitations. If there was actually an implicit promise that all classes are equalnone of this would be here.
4. Finally there is some guidance on party in the basic rules:
"Each character plays a role within a party, a group of adventurers working together for a common purpose. Teamwork and cooperation greatly improve your party’s chances to survive the many perils in the worlds of Dungeons & Dragons."
If I am to accept your argument that all classes are the same because of the CR tables then there would be no need for specific roles or cooperation. I would argue that the CR table is produced with the
implied understanding that this is how you are building your party. It is a CR table for an average cross-section of 3-5 member party.
This does not have much to do with balance. To suggest that magic users should be the most powerful is to suggest that there is no value in diversity. That the best party is one made up all of casters. Balance done well makes for a better game because it encourages diversity.
That is not true. The most powerful party would certainly be one made up entirely of casters (probably not all Wizards though). That does not make it the "best" though. The best party is the one that is most fun to play.
Balance done well makes for an awful game in my experience. I have never seen a homebrew rule for balance that actually improved the game and the only balanced version of D&D sucked IMO.
Now you can say that is anecdotal, but the opposite is anecdotal too and the statistical evidence we have does not show anything but it implicitly refutes the idea that a lack of power in the fighter class makes that class less fun to play.
No - they should be within certain bounds. D&D has among other things a strong element of randomness so two identical parties won't fare "the exact same".
Then why do we need to "balance" the classes? If randomness drives outcomes (and it does to a small degree), then imbalance is simply a bias on that random number generator.