To be honest, Skyrim isn't the first game to have done the "play whatever skills you want" style. Daggerfall (2nd game in The Elder Scrolls series for those unaware) was one of the earliest to have it that was successful and even they weren't the originators--that was some low budget indie game from way back in the earlier 1980's. The first Elder Scrolls game, Arena, was just a hack and slash game with Wizardry or Might & Magic style levelling.
My old Daggerfall char started out as the stealth archer because it was something I had never done and was insanely popular back then but not overpowered like the class is now. On my first runthrough of the game I ended up guildmaster of thief, fighter, mage guilds and max favor with 2 or 3 other temple factions. Of course my mage training consisted of going to an inn, renting a room for a week or so and practicing my skills then sleeping when I got enough points to rank up. After a few hours of this, I'd go back to the mage's guildhall and take a few quests to level up my faction reputation. I understand that this is still possible in all of the sequel Elder Scrolls games.