Every game is different. Flexibility isn't a good or bad thing. Chess is inflexible, and it's awesome. D&D is in the mid-range of flexibility. It is what it is.
Failed analogy. Chess is inflexible, sure, because it's not a RP game, but an abstract war game. RPGs in general need to be more flexible that chess. How flexible? Well, I believe we can agree that they need to be at least flexible enough to cover the needs of their genera. More flexibility wouldn't be a bad thing, but it might come with a cost in some other area.
And that's really where your analysis falls down. I don't agree that flexibility is in and of itself neutral. I think that it is a good thing all on its own. However, increased flexibility comes with costs. For example, increased flexibility in chess might comes with increased complexity, decreased focus of play, and decreased game balance. Since chess is a game that is intended to be an elegant two person competitive game, increasing flexibility at the cost of those strengths might be poor design. Chess for example has barely a page of rules. 3.X D&D on the other hand eventually reached a rule set in the 10's of thousands of pages, in part because it was prizing flexibility. 3.X gave tons of options to players to create all sorts of different archetypes. But it did so at the expense of increasing complexity, decreasing balance, and rules bloat - all of which are negatives in and of themselves.
If in fact you could achieve the same level of flexibility and freedom to play any archetype with a smaller rules set, that had more balance, this would in general be a good thing. One thousand different classes means 3000 different pages of rules all on its own. Yet a quick survey of the classes shows that the vast majority of them are very similar, and the vast majority of the PrC's in common use are even more simple. Further, a quick survey shows that many archetypes were revisited several times with slightly different mechanics often overlapping and stacking mechanics. And even if flexibility was in and of itself neutral, if that was the only way to bring it about, it would be on the net a negative.
Class systems themselves have good and bad features. If the class system becomes too costly, it's worth considering a skill based design. If your classes proliferate too much, it's worth considering taking two similar classes and merging them into a single class that can largely simulate either one through build choices. My feeling is that somewhere around 12-20 classes in your system (the exact number might depend on your other system details), you're doing it wrong and rather than keeping piling on the classes you need to revise your original classes.
In my opinion, in a system like 3.X that didn't happen for reasons that have nothing to do with good game design. First, there was the economic consideration - more pages of rules meant more books to sell and more profits. And secondly, they were in a situation where patching the system by extending it cost less than revising what was already out there to meet new standards. So while it was obvious from a very early point that the 3.X fighter had too conservative of a design, it was easier to replace or enhance the concept through extensions than revise the base class even though the later would have produced a better design.
The various reboots to 3.X (Pathfinder, 4e, 5e) all attempt to address that concern in their own way.
