In reality we class everything. It`s how we are for good or bad. Being a Policeman is a class, he doesn`t put out fires like a Fireman and a Fireman does not fight battles like a Soldier.
In reality, a Policeman can switch profession to Fireman if he wants. You could also start learning taekwondo and after having a good level in it, choose it doesn't suits you anymore and spend the rest of your life practicing archery, winning cups and all.
The class system is basically forbidding you any change. And what's terrible is that IRL it's exactly the problem of labeling people. Take the ex-footballer Eric Cantona (English people will know). He paints. Of course all the medias took it ironically, and everybody says "ah ha, a footballer who wants to be a painter!" With the class system, that kind of short-sighted vision of the world is set to rule. That's horrible.
And never anything wrong with starting a new game and having to choose skills you don't know for the rest of your character's days, for the whole game?
When you start a TES for the first time, either Morrowind or Oblivion, when you define your class, what do you do? Do you pick skills saying "hmmm Illusion that sounds nice, Conjuration I'm not sure let's toss a coin..." or do you pick a premade class thinking "Ok devs are giving it as an example, it must be balanced"?
Sure a great thing. As you like to link it to reality, did you choose your profession in the craddle? Did you really take the first profession you wanted to be as a child?
Those are rhetorical questions. The players asking for classes are often those stuck in the D&D system, speaking about paladins, cleric, etc. Never evolved and fear to lose their comfortable drawn path, even if it's totally absurd. Be a good wife : don't work, cook and raise the children. Outside is full of germs anyway.