The question is fundamentally unanswerable and it's a mistake to try to draw comparisons to the way modern weaponry is issued. Most societies with metal tools made some kind of sword, but it's not as if medieval chroniclers cared a huge deal about the exact casualty breakdowns of sword or axe wounds. It was common to carry several weapons and switch between them as the situation warranted. No knight would care about the distinction of "primary vs secondary" weapon when deciding whether to use his poleaxe, mace, sword, or dagger in a specific scenario.

Is there a specific era you're looking to learn about because sword usage will change from era to era.

Alright, so I don't have a fancy flair or anything, but this is totally my bread and butter. Keep in mind that the answer here is at least partially speculative (by virtue of there simply being missing information in the collective knowledge pool), and while referencing medieval Europe primarily, also uses information exterior to that continent and that time period. Cool, disclaimer over.

So, let's take your essential question:

How commonly were swords actually used in combat?

The first thing to do is to break down "combat", as combat comes in many different kinds. For instance, a friendly practice duel at a fencing school is essentially "combat", as is a village raid, a pitched battle, a siege, a street fight, and whatever you'd like to name. Certain weapons are going to be more accessible and/or appropriate in particular combat contexts. Understanding this goes a long way towards illuminating the purpose of a sword in just about any society that uses them.

The edge of just about any sword is more or less useless against plate harness, and of very limited use against mail armours and other metal protection below the development of plate. That's pretty bad -- most swords from most societies are really about the cut moreso than the thrust, and there's plenty of armour out there that was specifically designed to thwart cutting attacks. To be fair, however, that applies just as much to other cutting weapons as it does to swords -- the edge of a "normal" spear, while a reasonable cutting tool, is at least as stymied by metal armours as the edge of a sword is. Likewise, the edges of glaives, naginata, whatever. Hard, metal armour of many different kinds goes a long way towards protecting from the cuts of just about any weapon that can deliver cuts in the first place.

As much as this is a problem for swords, it's also a problem for a wide range of weapons. But not as big a problem as you might expect. Modern people tend to think of the function of a weapon in very visceral terms, such as the degree of injury it can cause, or the amount of material it can penetrate. Those are worthy, relevant considerations, but ultimately superficial in the face of strategy. You might have a kind of rifle ammunition that can punch through the hull of an aircraft carrier, but that makes very little difference if you can't safely enter into range of that carrier, right? Swords were useful because of strategic principles; because they could thrust, cut and bludgeon, and be used as swords or polearms, with shields or without shields, with a high level of design diversity, there was little a sword couldn't accomplish on a strategic level.

Remember, your goal is to defeat your enemy. Whether your enemy is dead is not often here nor there, and in some situations, it might even be preferable to defeat your opponent without killing them. Late medieval ransoming was one such case; a captured enemy knight represented eventual money in your pockets, whereas a dead enemy knight only represented the weapons and armour you could strip from their corpse. So it was generally better to take an enemy knight prisoner than it was to kill them -- it was better to defeat them moreso than kill them. While not all societies had comparable military paradigms to incentivise non-lethal means of winning combat, the knightly tradition of ransoming does prove a point; the defeat of an enemy can occur before the death of an enemy, and an opponent is defeated when they no longer hold the capacity to resist one's strength at arms. If one's objective is to kill an opponent, then that point of defeat also marks the point when the weapon once uses is no longer particularly relevant in terms of capacity to wound (that is, anything will do) -- but the weapon one uses can change when that point of defeat is reached. I hope that makes sense, because as I write this, I can see where it might become confusing or excessively abstract for those reading it.

To provide an example, the pyramid-like "blade" of a ballock dagger can penetrate mail quite well, and can penetrate plate under the right circumstances (such as when the target is braced against an object that prevents the impact dispersing properly, imposing additional pressure on the armour). Ergo, you have essentially defeated your opponent when you can attack a significant target on their body that has armour of mail effectiveness or less without sustaining a hit yourself. You can accomplish this a number of different ways; you might take advantage of geometric principles, or you might grapple them into submission, or some combination of any number of methods. The point is that you "win" when you can attack your opponent decisively without considerable threat to yourself. This is true of prehistoric combat, true of modern military conflict, and true of everything in between. It's probably true of any kind of violent conflict that will ever exist. The tool is ultimately less important than how you got to that point of victory from the perspective of strategy and tactics. After all, we typically don't discuss daggers when it comes to historical fencing and combat, but they were an absolutely critical part of both military and civilian kit in many different societies in many different locations and time periods.

The above begs the question of how this applies to the use of a sword. As my example, I'm going to use a late medieval, European cruciform sword. In your mind's eye, it might be one-handed or two-handed, or its blade might be tapered or have more uniform thickness. Those design elements are of minor concern here, though, and what's relevant is that you consider a sword with two edges, a point, and a relatively large crossguard. This kind of sword essentially makes four threats against an opponent; one with the point, one with each edge, and one with the hilt (that is, the pommel and the hand guard can be used offensively). To win against someone using this kind of sword, you ideally need to nullify all four of these threats while keeping at least one of your own threats "online". Let's have a hypothetical situation, and we'll say that you wore plate harness. Awesome -- you've pretty much nullified two of four threats, those being the edges. While your opponent can still slam the edge into your armour to apply impact trauma to the tissue underneath, that's relatively minor, and far from lethal. But there are still two threats to consider; the piercing point and the more bludgeoning-friendly hilt. Luckily enough, however, you're only really within range of one of those threats at a time. At longer ranges, the point might be able to get into your armour, but the hilt can't reach you; if the hilt can hit you, then you're probably too close to be threatened by a thrust to a gap in your armour. So by wearing your plate harness, you've turned four threats into, essentially, one shifting threat that can easily be judged by range.

But that's still a threat. You opponent has two possible solutions to the problem of your armour, and with skill and strategy, they can fight you into a position where you're vulnerable to a decisive attack. They might lever your weapon out of the way during the bind and use that contact as a position of stability from which to thrust into an armpit, or under the chin. They might beat your weapon out of the way and come back with a pommel strike to the temple. The plate harness you wear is designed to overcome swords (and other things, but particularly swords), but it can still lose to the technology it was designed to overshadow.