It's not really about the strength of holding the weapon, it's what you are able to put into the weapon, and with what technique. When using a single sword, like the Samurais did, you can do fast swings with one hand, but put all your body into the one sword when needed for extra force. Also, you can focus on that one sword and its movement instead of keeping track of two swords + enemies + your own feet + surroundings + etc.
In the good old days, dual-wielders were rare and far between. It's just not practical compared to a shield, spear or two-handed weapons, simply because there were no "adventurers". These were soldiers with specific purposes, not all-rounders, so people with shields needed them to deflect arrows, those with 2h weapons went up against heavy armored opponents, and those with spear were needed against chavalry.
Of course, this is very simplified, but the point is - dual-wielding in general may have been used by certain gladiators and such, for duals perhaps, but in the middle of a war? Not really, there are better things to do.