Likely repeating what has been said, but...
Ambidexterity doesn't mean you can fight with two weapons at once. It means you can fight with the same weapon in either hand, individually, just as well. As someone who has participated in amateur sword-fighting, I can confidently say those two things are not remotely the same. Even if it were, it's more a question of balance in my opinion.
So how we treat it is you have to learn a weapon in a specific hand. Ambidexterity does away with that need. But you still need to develop two-weapon style to fight effectively with both. If you are using two of the same weapon, you benefit. If not, you don't. Although, if you use different weapons you can potentially switch back and forth without a drawback - not sure if that'd come into play too often (maybe a sword with a wrap around hand guard intended for a specific hand).
My personal general rule is you cannot fight with two long swords (Broadsword for example). So you need to fight with, say, a Broadsword and Short Sword, 2 Short Swords, Short Sword and Dagger, 2 Daggers, etc.