I don't know, I think a lot of people are forgetting the state of the game when 3e was designed.
First and foremost, AD&D wasn't designed so much as assembled over the course of a decade or more. By the time of the 1990s, it was
very clear to the RPG design community that AD&D was the antithesis of a designed game. It was also a dead game as far as sales. People I've talked to in the industry at the time legitimately thought that everyone had moved on from D&D to other, more narrative games. And it's not hard to see why. AD&D is, more than anything else, extremely
arcane. It's full of dozens of systems and mechanics that each work differently, often contradicting each other. It's impossible to intuit or get a feel for how things are
supposed to work because it was all rules tacked on to OD&D. It was like design by Katamari Damacy. Attempts by TSR to add design to it in the form of 2e and Skills and Powers largely just fractured the game even further with even
more ad hoc systems. Worse, because the mechanical systems were so different, it was nearly impossible to tell from the mechanics alone what the true intent of each system was. Further, there was also a very strong culture of DM vs PC, perhaps best satirized in Knights of the Dinner Table, that virtually everyone recognized as toxic but was hard to undo. The nature of the rules encouraged an extreme number of house rules to be adopted. The complaint was that you couldn't go from one table to another because every table not only used different house rules, they used different subsets of the core game's rules, too! Different choices for initiative, weapon speed, weapon type vs AC, double specialization, warrior "sweep", grappling, level limits, race limits, XP determination, advancement, treasure placement, etc.
So, you're WotC. You've just bought TSR's IP, and you need to sell a new edition to justify that purchase. You can see that even though they were producing a ton of content, nothing was really selling. And the people buying were often just reading the content and not using it for a game. That's fine for making money for that product, but it means you're not producing content for your core customer base target. (They were also selling at a loss, but, still. Sales weren't
great and they weren't selling to gamers, their target audience.) WotC does a massive market study, and they find some really interesting and useful things like: (1) a ton of people still play AD&D but they just stopped buying stuff, (2) people like 3-4 encounters per day because it fits well into a session, (3) people don't play much over level 10, (4) group sizes are about 3-5 players plus a DM, (5) most groups ignore arbitrary limits (ability, level, and race), (6) nobody really likes alignment
that much, (7) people want to be able to find games easier, (8) people didn't really like Vancian casting, (9) non-combat should be expanded, (10) players didn't like not having any agency, (11) players wanted more customization and options, (12) nobody likes being "stuck" playing a cleric or thief, (13) save or die is not fun, etc. Unsurprisingly, all the stuff that they found was either a core design element of 5e, or is something that people still complain about in 5e. [You used to be able to find articles by Monte Cook, Sean Reynolds, Skip Williams, etc. about this big survey or research that they had done, but they're very hard to find now. Some were probably on Eric Noah's original news site, although many weren't written until well after 3e was published.]
Other than that, what WotC really finds is that
nobody uses the rules as presented. It's all a big mix of a la carte choices. They thought they'd be dealing with 2-3 different versions (Basic, 1e, 2e) but what they're actually finding is much closer to
dozens of "editions". And the reason WotC comes up with is: there's no cohesive design. Lots of rules are too complex and time-consuming for most tables to bother with, or they're actively not fun, or they just don't work.
So, your new edition needs a cohesive design. That, right off the bat, says you need a brand new system with many core mechanics completely redesigned. That's question 1. Question 2 is: What rules do you incorporate into the new edition to satisfy as many people as possible? When everyone is using a different subset, what do you pick to attract the most existing and new customers? Think about that a minute. You need to redesign the game, and you can't tell what game people
actually play! This is
by far the most difficult question to answer with the new design, and even looking back and knowing the flaws, it's hard to say if what they ended up doing was right or wrong. They
couldn't tell what was actually important. Even for us looking back, we can't tell if a different design would have attracted fewer players or failed for other reasons. Nobody had really done before what 3e did in the sense of scope and scale of rules for a TTRPG. So, as we all know, they decided to make the
most cohesive and complete design they could, incorporating as much material as possible. Knowing from the start that they would have to create another new edition in perhaps only a few years to fix the big mistakes (and to again offset the cost of TSR), this seemed like the best course of action. At the very least, it would let them tell what people actually used and pare it down in the future.
Therefore, the primary purpose of 3e was to give it
a design. An actual game designed by professional game designers, not hobbyists with boutique, hand-crafted systems for everything. It wasn't going to be perfect but, given the sea of chaos they began with, 3e just needed to be the seed crystal to making an actual RPG product out of the IP. Because what they bought didn't really have that.
So, to answer OP's question: The class design of 3e was intended to replace the AD&D designs in terms of class ability requirements, racial restrictions, racial level limits, and resolving dual class vs multiclass. Otherwise, they were the classes you were expected to use for the whole game.
The unintended consequences were:
- People ignored the or easily circumvented the multiclass penalty of Favored Class. It was intended to be a weak restriction anyways, but it enabled a la carte multiclassing to take advantage of class ability frontloading. That's why in 5e nobody gets much of anything cool until level 3, and it's why warlock is such a bad design (the class plateaus progression between level 3 and level 9).
- People really, really, liked the new kits: prestige classes. These were intended to be 1-2 available as determined by the DM for a given campaign as a special reward. Nope. Everybody wanted a prestige class for their character in every campaign for more cool abilities. So, very quickly with the introduction of splat, the base classes became a puzzle to answer the question, "How do I optimally get to my prestige class as quickly and efficiently as possible because the game is still probably going to end between levels 6 and 10?"
- Spellcaster scaling really, really got clearly out-of-hand. The problem Gygax knew about in Supplement I in 1975 had grown into a tarrasque-sized problem in 2001. It became very clear that the way casters worked was grossly unfair, but it was an unfixable problem without another major edition to totally overhaul the game.
So, much like 2e, the big problems with 3e class design were:
In 5e, I think kits is pretty well handled. I think LFQW is mostly handled, but possibly a little over-corrected with how unusably bad some spells are now. I think multiclassing is still mostly a problem.