The problem with TES fans is that they are over-zealous about certain things - just because they have been used in most of the games released so far. Okay, so I understand it's important to stay true to the lore (because that is what Bethesda refer to and gives the world an authentic sense of consistency); but I do not understand why people would object to a TES game using a class-system or skill-system such as that in Fallout:New Vegas.
I like Fallout New Vegas' skill-system - mainly because you can't really become an expert in all trades. In real life, you don't find people becoming experts in all trades and people specialise. Some people are naturally more talented than others; regardless of amount of effort.
And yes, the issue of replayability is brought up. Some may argue that the player should choose restraint if he wants to prevent his character from becoming "jack of all trades" - but that defeats the immersion. The reason it defeats the immersion is that characters of a certain educational background or life experience may find it MUCH HARDER to grasp and deal with certain skills/situations than others. So yes, I think "class" could be a substitute for personality type or assumed experience after character creation.
I also think all classes should have basic skills (including knowledge of basic spells). But I think it should be much harder to get to higher levels in the ones that your chosen character is not comfortable with. For example, I know how to cook and I know enough math to get me about - but i have ZERO motivation for advanced mathematics at the bleeding-edge of cosmic physics, and i function much better at language skills and art, etc. I have friends who are great computer scientists, but they couldn't write beautiful poetry to save their life and neither do they have the psychological history or motivation to learn or delve into that area. If they wanted to, they'd find it difficult. This is just the nature of things - only rarely do we have people find that learning all the different things in the world are equally easy.