Most soldiers, only had standard issue weapons. As they, or their lord, or country, only had enough money to give them what they needed, not what they wanted. Which in most cases ment a primary and if you were lucky, a secondary weapon. Most commonly the secondary weapon was a knife, or dagger, or fork that was used as an eating utensil, shovel, comb, razor.

By and large fighting with two weapons made for clumsy combat and as most SCA fanbois will comment, fighting with a shield is about 100x more effective, though it doesn't look cool

Most of the ambidexterous units in the game at current are rare. Only a particular type are given it (Bane Spider, Lava Warrior, Warlord, etc) I don't think it would be all that unfathomable to have the monks and the ninjas dual wield, but not every elite unit they have.

Also, just a footnote. Most samurai used naginata as their primary weapon, from either horseback or on foot as it afforded them both reach to fight either type of troop (cavalry or foot) and ease of training as well as being able to bash things they couldn't cut.