It's the choice that is equally weighted. What do you have to do to play a fighter in 5e vs a wizard. Just pick one. The choices are equally weighted. Now, if D&D were a build system, where you got 99 points to spend on your stats, background, race, and class, and fighter cost 10 points and wizard 29, they would be differently-weighted choices.
Since D&D classes are equally weighted choices, the fact they sort into starkly different 'Tiers' is evidence the game is badly imbalanced.
If there's an acknowledgment that the classes aren't equally weighted (i.e. that they are divided into tiers), then I'd say that by definition means that they
aren't weighted equally. It's like comparing paper money (in the U.S.), where the bills are the same size and weight, but have different denominations.
Not at all. Genres and campaigns have scope, tropes and themes. The range of possible scenarios may be huge, if you consider them in enough detail, but they fall into the scope of the game - fighting 6 goblins a 20x25 room is different from fighting 7 goblins in 35x20 room, but they're both combats. The game, itself, also provides parameters in what it chooses to model, and how, and what it chooses to simplify, gloss over, or kick to the DM to fake in the moment.
I don't believe this to be the case; even on paper that strikes me as an oversimplification of what the game allows for, and quite often what it's composed of, even if we leave aside the fact that things change depending on what specific enemies are faced under what specific circumstances and after how many previous encounters (which conceivably changes, possibly dramatically, what the PCs are capable of). Facing six goblins in a small room is very different from fighting a half-red aquatic great wyrm in its undersea volcanic lair which is itself in a natural dead-magic zone (and yes, I speak from experience there).
The scope of potential play is too wide, in other words, to be narrowed down by the examples your outlining, and the parameters themselves are little more than (very loose) guidelines which are all too often treated with more weight than they were ever meant to have (i.e. "you're
supposed to face four encounters per day of a CR equal to the average party level!"). That's a design principle to allow for eyeballing things, not an exact science.
The three pillars contextualize what happens a game like D&D well enough to determine how abilities compare in a range of situations, for instance.
I disagree here also; at least two of the three pillars strike me as being highly overstated, to the point where in many cases they're a myth more than a reliable indicator of, well, anything (insofar as being able to systematize interactions with them for balance purposes goes, I mean).
A game that tries to equally-weight choices that are useful only in radically different situations is going to be badly balanced across, say, a whole campaign. The way, for instance, that fighters receive Extra Attack as a major portion of their effectiveness, useful only in one pillar, while spells are at least as useful in combat, and also in the other two pillars is another solid example of bad balance.
That's largely because you can't delineate comparable options across a spectrum that consists of "anything." Again, this is why I think verisimilitude is a much better measure to go by than a nebulous concept of "balance," because the former allows for the PCs to measure the situation in-and-of itself and make choices therein with what they have at their disposal, applying it against what they know with regard to how/why the world works the way it does. It's much better than the one-size-fits-all method (I think) that "balance" keeps shooting for, but doesn't ever seem to come close to without having to eliminate a lot of options (often in a way that impinges on verisimilitude; again, chess is a very well-balanced game, but it makes for poor role-playing).
