Dual wielding is not necessary as an assassin because your initial damage should be so huge that if they are not dead from it, they should be close to it.
But I dual wield as an assassin for the convenience. My right weapon is for normal sneak attacks. My left weapon is for trapping souls.
True, as an assassin/rogue character, my stealth attack damage is absurdly strong - no problems there. But, unless i'm mistaken, it would be nearly impossible to sneak up on a dragon in a normal encounter without using invisibility. I want a light armored, thief-type character that can ALSO go toe-to-toe with a dragon if necessary, and it sounds like dual-wield was not intended for that purpose. It almost seems that dual wield is the combat style most dependent on other skills in order to realize a well-rounded character, such as someone above mentioned, using enchanting/smithing to increase damage and stamina, or using sneak attack exclusively, or improving light armor to reach the damage reduction threshold.
But, just dual-wielding on its own, in a straight-up fight at earlier levels, simply isn't as viable it seems.