Which is probably one of the principal reasons why they dumped the system.
I'd agree there, I'd consider upgrading skills without it counting towards leveling one of the flaws of the class system in the Elder Scrolls, because it was very easy to exploit in order to allow players to get very high attribute multipliers in all attributes, and combined with level scaling in Oblivion, allowed for, even encouraged an unnatural play-style where players would intentionally set most of the skills they actually intend to use regularly as minor skills, thus allowing them to raise these skills very high without causing enemies to level up.
I don't really mind the absence of classes, myself, as they didn't seem all that important in past games anyway, the main difference they made in the long run was determine what skills let you level up, and that mostly seemed to cause exploits, so I don't mind that Bethesda has chosen to remove classes. I'm not sure if I'll like the new character system better or not, but I'm not going to object to it just because it involves removing classes.
As to labeling classes, I honestly didn't care about that at all, I don't need a label to tell me what kind of character I want to play, indeed, not having the label might have its advantages as I feel more comfortable playing my character in the way that feels right, which isn't always what I planned for when I initially created my character, if I create the class I want to play for a character and then name that class a certain name, then I end up not playing the character according to that name, it feels a little odd, and in the end, I often just didn't bother naming my classes, just "Adventurer" describes what my characters usually do pretty well anyway.
Really, the main problem I could see not having classes causing would be that classes in the Elder Scrolls also allowed you to define what skills and attributes started higher for you, as your major skills and favored attributes started higher for other ones, which helps to reflect that your character may have already been better at some things than others before the start of the game. But this could also be adressed by introducing something similar to how "tagged" skills worked in Fallout 3, in other words, allowing you to choose some skills at the start which would be higher than others. Or if they want to give you more freedom in character creation, allow the player to distribute a certain amount of skill points freely among skills to raise your starting skills, enough to give you some room for customization, but not enough to raise your skills really high early on.
ARE YOU SERIOUS!? THEY ARE GETTING RID OF CLASSES!!!!!!!!!!!? Are they seriously going to make it so that everybody can do everything?
You can already do that in both Morrowind and Oblivion, and getting rid of classes doesn't necessarily mean anyone can do everything, lots of RPGs don't have classes and still don't end up with players mastering all skills, Fallout is one example, with the possible exception of Fallout 3, mostly with Broken Steel since it raised the level cap ten levels above what the game was originally meant to have. Really, with or without a class system, it all comes down to how the game is balanced, removing the class system just means that your character's abilities are defined by how you choose to develop your character over the course of the game, not which class you select at the start.