What the new system succeeded in doing was delaying when your character gets "locked in" to his class. Once you reach a certain point in the game, you have taken so many perks in a particular specialization that it is now essentially your Class. The game doesn't label it, but there is still a class system in place. Whether intentionally or unintentionally is not for me to judge, but there does come that point in the game where you have taken so many perks in one particular specialization that switching to another would result in a character that is only "OK" in two specializations instead of master of one.
Not that that is a bad thing, of course.

In short, the "no class" argument is invalid, because classes still exist. You don't need an arbitrary label telling you "this is your class" to tell you what your character is and is not good at, like in the real world, that is something you figure out for yourself.
Thank you.
.........
As far as 'dumbing' down, or streamlining or mainstreaming...
Many of the decisions made for Skyrim had to be different because of the introduction of the dual-wielding mechanic, and the region. I wish quests were more narrative driven, though some are quite heavy in that department, and I wish that you couldn't become the leader of every guild with one character.
I don't like, or rather... I don't think that weapons are quite diverse enough in 1H'd or 2H'd. They do different damages and swing at different speeds, but I'd like more definition.
The difference between 2H'd and 1H'd mobiles in this game is an improvement in this game thanks to finishers, where before a mobile just swung his enormous claymore at your face and it just didn't seem that a weapon of that calibur conveyed the brutality of being hit by a weapon like that. I enjoy knowing that if I go up to a Bandit Chief wielding an enormous Warhammer... I may very well get my skull crushed at any time... and god help me that just seems
right.
The thing you have to remember, which really puts this whole 'dumbing down' discussion into perspective is this :
Dual-Wielding is a spanky new combat mechanic to TES, and it should be no surprise that there are going to be some mistakes made with a
brand new system. If those mistakes translate to streamlining, or if the steps taken for balance translate to 'dumbing' down... well that is entirely opinion.
There are perks in the armor trees to reduce armor weight and increase your speed and reduce fall damage, there are perks in 1H'd to increase swing speed, and so athletics remains... sort of.
The Magical school of Mysticism? Redundant, and quite honestly... illogical. Definitely glad that got scrapped and merged.
Levitation? Don't even get me started on the logistics of this in a mountain range, or just being able to fly directly to the Throat of the World.
Spell making? Dual-wielding provides a sort of replacement, but there is definitely room for improvement. I would like to see it come back I guess.
People don't like change, but TES has to change... or risk becoming stale and irrelevant.