Our characters weren't born just prior to getting on that wagon. They had their entire lives before that.
About the wagon, it's absurd to say your character is born just before being the wagon because every characters starts the same. The characters start as "a nobody in a strange situation" in every single TES. The theme of the prisoner is always there because TES games are humorous too. There's always been jokes that some players don't take well because "it breaks the immersion" when it doesn't break the fourth wall. But anyway, the character coming from nowhere is great because the point isn't to let people write novels about what their character was before but the point is we don't care. The character wasn't developped more than the commoner with just his racial traits. His adventure truly begins there. For TES, the authors have always decided to skip the presentation of the ordinary world of the character and jump to the triggering factor. This has absolutely no consequence nor is it influenced by the fact that the game use a class-based or free-to-build system.
The few points you earn by choosing major skills is merely a candy as an excuse for chaining you to that choice the rest of your character's life. They can't represent a life-long choice before being prisoner, because that's a few of the easier to gain and while playing the game you will gain in a few day more levels than your whole life before being prisoner. It's absurd. Even in Morrowind you could easily raise your minor skills above the starting level of major ones. How will you explain that? Your character was a [censored] prior to the exile to Vvardenfell? Again, as in my previous point, we don't care about your past. We're not going to try to explain it. TES isn't that serious, or uptight like some players are.
You want another proof that being class-based or not doesn't change anything on the believability of the past of your character or his uniqueness? In Oblivion you actually started just like in Skyrim. Isn't it ironic?
In fact that was the first step from Bethesda to make the decision of what your character would be less stupid. They knew it was totally awkward to ask which skills you'd want with such precision as major, intermediate and minor. The player : "I have no f idea how your game works, how am I supposed to sort skills in such categories?"
So they created a tutorial for you to test the skills and have an idea before choosing. The sewers. But of course it's far from being a smart design, as you still don't have much idea what are all those skills and if they'll really be useful to you specifically. And the tutorial can't last two hours just to present you everything. So with Skyrim they give you everything, you test out what you want and you keep what you like to create the character you want instead of the character you thought was possible to make.
And that leads us to another funny point after the players blocked on the D&D system. Most of players don't start playing a RPG with a character of its universe that will adventure in that universe, they take a character they like, that they play in every single RPG and try to develop it again in that new RPG universe. The name is taken from a fiction they liked, the philosophy can be from another, etc. Sometimes it doesn't come from a movie or a book, but it comes from the character they built in another RPG.
With that in mind, lots of players don't even bother knowing which skill do what, they pick the skills that sounds the closer to that character they always play. When they are stuck with a crappy class (if the game allows customization), they deny it and prefer saying that's the way they wanted to play their character, for roleplay. Or that the game is bad. That's only denial. I started with a Bosmer Archer in Morrowind because I liked the idea of a wood elf hunter, knowing the nature and shooting arrows in the forest. Fortunately I quickly got closure for that idea, abandonned the crippled bow and took advantage of the blade skill that this preset class had. I went through the game with a daedric claymore and everything was better. That skill saved my character.
I did almost the same mistake in Oblivion, believing that this time archery would be better and that it would combine well with alchemy for poisons. That preconceived character was so pathetic that it lived only because that was a character I wanted to like. Then I accepted my mistake and trashed it. Because there were no other solution. No way to reconvert, to change class, to change your character's life. You chose a wrong path? Enjoy it to the end (ie your character's suicide).
How is that better than my experience in Skyrim where I was able to adjust my character style to the reality of the game instead of having a shameful character and keeping it because theorically it should be otherwise. There's a moment all the fiction you weave around your character has to actually fit in the game, not just in your dreams. Between instant gratification fun and writing a novel, there's a world of possibilities. Some players are too much on the first side and toss the game because it's not balanced, some toss the game because it doesn't fit in their own stories... but the existence of the game has to be in-between. Let the game give you the tools for a story and use them for fun. It's not a super-duper-serious game.

