While these swords are really cool to look at, it seems like it would require an incredible amount of extra labour to produce a weapon with a wavy blade instead of a straight one, and I can't imagine that there wouldn't also be any structural tradeoffs in aiming for that shape.
Was there an advantage to their use that made up for all the extra work that had to go into them (and potentially any other tradeoffs), or were they something like a decorative piece meant to show off a smith's skills or the wealth of whomever could afford to have one commissioned?
Are there any historical examples of them actually being used?
It certainly was expensive to produce a blade like that, great swords were already generally on the more expensive side of weapons and flameblades took it a step further. On the subject of structural strength that doesn't seem to have been an especially great problem, historical treatises ever seem to complain on the subject at least but there were other things that do come up. Normally you'd rest such a blade on your shoulder and walk around with it like that and the flamberges might accidently nick yourself in the neck. Additionally perhaps it wasn't quite as easy to drive between a a narrow gap in plate armour.
It does have some notable advantages though in terms of the cutting power produced in certain strokes with it, the curves in the wavy blade edge reduces the contact area at the moment the blade strikes potentially increasing how easily it could cut through the target while the almost sawing motion of the blade driven into the target then pulled free would have no doubt produce a wound that'd be particularly likely to incapacitate its victim swiftly.
The other thing is given the stereotypical reputation of men like Landsknechte looking really cool could certainly have been an important motivation for them, they were known for some fashion styles that bordered on the impractical like comically large cod pieces along with things like brightly coloured clothing. Meanwhile men with such great swords who had been trained by certified swordsmasters in that art earned double pay so its likely at least some of the men who'd also gotten some good loot would be willing and eager to buy a sword that looked awesome. Baring in mind things like the push of pike was as much a psychological battle as it was a physical one and being dressed to the nines and looking like you really knew your business was part of the way a regiment displayed its reputation to maximise the chance that when the drums went hammering away and the pike squares marched into each other their opposite number would decide they'd just remembered they'd left he stove on.
The short answer: Yes.
The three main places where we find wavy-bladed swords are Europe (mostly large two-handed swords, some rapiers, and some other types of swords), India and Persia, and SE Asia. In Europe, the large wavy-bladed two-handed swords are usually parade/ceremonial/display swords. The large two-handed sword was a relatively rare weapon on the battlefield even at the height of its popularity - while Landsknechts are the best known users, most Landsknechts were armed with pikes, guns, or halberds (and most double-pay Landsknechts were armoured pikemen). Contemporary art of Landsknechts with two-handed swords almost always shows straight-bladed swords, not wavy-bladed swords. Of the surviving wavy-bladed two-handers, many are of the more ornate and/or very heavy types used as parade/ceremonial weapons, rather than battlefield weapons.
However, there is no reason to think that none of the rapiers (or left-hand daggers) with wavy blades were used in duels. The main function of ornate rapiers was display, but they were used as duelling weapons, too. As weapons that were often used to display wealth and taste, the greater expense of a wavy blade might even have been an advantage.
Another class of European wavy-bladed swords is boar-swords - two-handed swords with wide tips, for hunting. Some of these board swords have wavy-bladed tips. Again, as rich men's hunting weapons, partly functioning for the display of wealth and taste, the expense would not be a problem. There is no reason to think that these wavy boar swords were not used (but for hunting, not war or duels). Interestingly, there are also wavy-bladed plug bayonets, possibly also for hunting. Some wavy boar swords and plug bayonets can be seen at:
Old Indian and Persian wavy-bladed swords are often ornate, and appear to be upper-class weapons. Apart from the waviness, they are similar to conventional weapons. That is, we see wavy shamshirs, wavy katars, etc. There is no reason to think that these were for display only; they probably would have accompanied their owners onto battlefields, and might have been used. But they would not have been common weapons on the battlefield.
So far, none of the weapons considered would have been commonly used in combat. The wavy large two-handed swords in Europe were mostly for display; their battlefield brethren were usually straight-bladed. Other than these, the wavy weapons are a minority compared to non-wavy versions of the same weapons, and they would have been rare in duels and on the battlefield. However, in SE Asia, we find a weapon that was frequency wavy: the keris or kris. The keris/kris covers two distinct weapons: the relatively small stabbing dagger of Indonesia and Malaysia, and the Moro kris of the southern Philippines, a robust cutting sword. Not all are wavy, but wavy-bladed examples are common.
The Indonesian keris did see use on the battlefield, as a sidearm. It also saw use in combat in duels, and as an emergency self-defence weapon. The Moro kris (and other traditional Moro swords) saw use on the battlefield into the 20th century, in the Moro Rebellion (part of the Philippine-American War). By this time, guns had long since replaced swords as the main weapons on the battlefield, but swords did still see some use in combat. Some wavy-blade Moro krisses can be seen in:
The waves are not always functional when it comes to fighting. Some wavy-bladed krisses only have waves at the base of the blade:
and the distal half of the blade - which is the part that will usually be used for cutting - is straight. If it was felt that waviness offered a significant advantage when it came to cutting or thrusting, these half-wavy weapons would be difficult to explain - the maker went to the difficulty and extra work to make a wavy blade, but left the part used for cutting and thrusting straight.
