So with no set skills... Mid way through a game you could ditch that two handed axe and dwell into destruction magic. Since you can "do more" with one character do you think this will limit how many times you create new characters?
The issue with that is they've already said that higher leveled skills level faster than lower leveled skills. In addition, higher leveled skills contribute more to leveling up than lower leveled skills. Thus, once you get deep into a leveling a skill up, it is wise to continue using that skill, as switching to a less often used skill would both slow your leveling down and also level far slower. You would also be less proficient in that skill and may be fighting rather strong enemies, depending on how the level scaling is handled in Skyrim.
Also, don't let the lack of class skill sets confuse you. You could do the exact same thing you just described in Daggerfall, Morrowind, and Oblivion, the only difference is that you wouldn't level up from using skills that weren't major/minor (or just major, in Oblivion). The only difference now is that you do level up from using skills that you don't use often, you just level up very slowly.
In addition, remember that they claimed that the level 50 of Skyrim is about equivalent to the level 25 of Oblivion. You also stop getting perks after level 50. Thus, you will ALWAYS miss out on a lot of perks, and switching to start leveling up a different skill set would cause you to miss perks in both your old skill and your new skill, depending on your level. It only gets worse the more skills you drop and the more you pick up to start using. If you switch in the middle of the game like that, you may find yourself hitting level 50 with no "ultimate" perks (as in, the highest perk in the tree, and also probably the most powerful/interesting).
So, you could feel free to switch over, but you may find yourself lacking in power or diversity.