One thing you have to bare in mind about why sword and dagger fighting is that it was the techniques and common use of such things primarily evolved surrounding the context of things like civilian weapons carry as opposed to being the norm for battlefield combat. In the context of a gentleman going about his day any weapons that he might carry for the purpose of things like self defence, fashion, duelling ect are going to be selected not with the fighting qualities of the weapon alone in mind but also considering things like prioritising weapons that were socially acceptable to carry and comfortable to carry while keeping the hands free for other things. And so if i want to say go have a walk in the city or i need to spend some time travelling its less likely that I'm going to carry something as large as a pike or halberd, or arquebus than something like a dagger which was very commonly worn as a utility item anyway by people of a wide variety of backgrounds and of which variants like parrying daggers and otherwise specifically made left hand daggers. And then if you were perhaps a little wealthier, maybe had more reason to expect trouble you might weapon a side sword or rapier. Just something that can be comfortably worn on hip and was more likely to be considered fashionable and be legal and socially acceptable to wear in more places compared to say a mace.

But the point i'm trying to make his is partly that sword and dagger fighting styles emerge in no small part to make the most out of the kinds of smaller more socially acceptable weapons someone might carry in a civilian context, in a context where carrying weapons more warlike than swords was acceptable either in the context of a dangerous journey, different social contexts surrounding weapons or just a particularly dangerous civilian context it was more common for someone to use instead of a dagger or a second weapon of a similar size either a shield, handgun or a longer two handed weapon like a polearm, bow, long armed fire arm or two handed sword of axe. All of these could arguably provide greater utility in the majority of circumstances than using two weapons and was the norm even in places where two weapon fighting with other weapons occasionally occurred.

For a shield for example while a parrying dagger or a sword in the off hand could be used primarily defensively while a weapon in the main hand could be used mainly offensively but it still doesn't provide as good protection from missiles nor fending off the point of a spear or the like, an axe in particular lacking hand protection could be used to block but doing so left your fingers somewhat in peril. The benefits of having a handgun instead of a second weapon in the off hand seem pretty obvious, its a weapon that can still be used somewhat in close quarters or at a slightly longer range to take out a threat and many designs of weapons like flintlocks and wheel locks where pretty chunky so they could still be used as a blunt object if necessary once expended which there is fairly regular artistic depictions of in the context of things like boarding actions. A longer weapon then allows you several benefits that having a second single handed weapon does not. Polearms and other two handed melee weapons might well provide you with additional reach, plus it would allow you to put more force into a strike in order to defeat certain kinds of armour and have the strength to do things like lock or or force out of the way a longer polearm someone else is using. Then of course bows and long arms are going to require two hands to operate and while you can throw a javelin or use a sling one handed ideally you'd tend to have spares in the other hands or otherwise in a manner that allows you to use you other hand to help load the sling which you could also do with a shield strapped to your arm.

For example with the sagas you have to bare in mind that while the sagas can represent a useful source to at least consider that the written documents we have were all made a good while after the viking age ended and the events they depict and they are stories. Tales that might well have put a few dramatic flairs in there. And so even in that context fighting with two axes isn't portrayed as something that's common, its a great heroic act as opposed to the norm of fighting primarily with weapons like spear and shields. There are occasional artistic depictions of fighting with two swords from the medieval period but again this certainly isn't supposed to be something we should interpret as the norm.

I am aware of various eastern traditions that include two weapon fighting more often, i don't have as much relieving expertise to comment in depth but i don't get the impression that these where the norm in warfare even in periods where weapons like butterfly swords where more common.