While I generally agree with you and your posts, this is a dealbreaker. A "classless D&D" is a different game. I don't know what it is...and I do not deny they could certainly make such a game and slap a D&D logo on it. But it would no longer be the D&D we know...or I want to play.
To some people, there's another kind of niche protection; the niche that D&D occupies as being distinct from other rpgs. I don't believe much in that one either. To me, when I'm running CoC or Cortex (generally my non-D&D choices) or when I'm experimenting with something else, that's still "playing D&D".
To me, D&D is a creative medium; the sine qua non is the idea of a group of people with one in charge and the others adopting the roles of specific characters. Fantasy is part of the deal, but not essential. Killing things and taking their stuff is part of the deal, but not essential. Likewise, six ability scores, quasi-Vancian magic, and a fairly standard retinue of classes are part of the deal, but not essential. I'd miss the ability scores more.
Moreover, let's (oh joy) consider 4e. It establishes roles and creates new niches that didn't previously exist, carving them out more discretely than 2e or 3e. By doing so, it became, in the eyes of no small number of people, un-D&D. D&D classes often (always?) don't occupy one niche, and trying to force them into one seems more unnatural to me than losing them altogether.
How does this not confer niche protection? If the fighter can cast spells and the wizard can wear armor...then where's the niche? By definition, a class-based system must provide classes with niche protection, to some degree.
In practice, it still does, but it doesn't have to.
For simplicity's sake, let's say we have a new skill-based system, where attack bonus, hp, saves, AC, and caster level have been subsumed with skills and feats. A character starts with 10 points. One could design a "fighter" that automatically spends eight points in the stuff fighters do, attack, saves, health, whatever, and then two left unspent for the player's choice. The player could spend those last points on the good ol' Intimidate and Swim just like a 3e fighter does, or he could spend them on picking up thief skills or magic.
And the class itself might be optional, functioning much like a starting kit in 3e. If you want to trade in some of the fighter stuff, you simply subtract points in the things you decide you no longer want, and add them elsewhere.
3e is almost like this, but not quite, because there are some things that are not available as feats and skills. For those parts of the game that are (which include some things that used to be class-specific), 3e/PF works exactly as I described.
I...do.

I guess. I dunno. It seems very natural and obvious to me...even if I'm not describing or defending it clearly/well.
I can imagine several possible rationales, but I can also imagine tearing them down pretty easily. To me, the real reason we use classes is the same as the reason we do many things in life, the reason why we eat the diets we eat, do the work we do, treat people the way we treat them.
Habit.