I saw a post of yours where you talk about flamberge blades, and how they existed for the twin purposes of looking cool and of making parries parties uncomfortable, but you left out one thing (albeit something most people leave out): they can simply have more stopping power than a normal blade. As it goes in on the thrust, the waves slice up and down through the flesh (especially if the hand rotates), causing internal lacerations and, thus, a fair deal more bleeding and/or muscular damage.
The reason why “flamberge blade = increased stopping power” isn’t usually mentioned is because it’s not given much credence except on the internet.
I’ve just looked through a baker’s dozen of my books, and only one - “Swords and Daggers” (Frederick Wilkinson © 1967) - says anything about flamberge blades causing extra damage. Even then Wilkinson goes no further than speculating “was believed to” with reference to cut, not thrust. The other books don’t say a word about it.
”Flamboyant blade” is a correct alternative to “flamberge blade” and a lot of historians seem to prefer it. There’s fair reason: in the 17th century “flamberge / flambard” meant a particular style of rapier with a dish hilt, and for extra confusion these rapiers usually had straight blades.
Despite all the on-line forensic descriptions of “more damage this / harder to stitch that / internal lacerations the other”, none ever go on to explain why, if flamberge blades were so much better, so few weapons in the whole of history were shaped that way.
Khopesh; gladius; Viking sword; Knightly sword; claymore two-hand; claymore basket-hilt; katana; 1796 Light Cavalry sabre; Bowie knife; Ka-Bar fighting knife; Fairbairn-Sykes Commando dagger - all famously good at cutting or thrusting, yet not one with a flamberge blade.
In three centuries of bayonets-of-all-nations, a few 17th-century plug bayonets like these are the only ones I know of, and they all seem private-purchase, not issue, and some historians think they were for hunting, not war…
The hunting theory may be based on boar-swords like this…
…though yet again, an image search turned up far more plain blades.
The single historical popularity-blip was the Zweihänder, a sword which seems to have a flamberge blade more often than any other kind of sword. Were there more flamberge Zweihänders than straight ones? I don’t know; but I doubt it. Modern survival doesn’t mean period popularity.
Maybe in-period they were “believed to be” more effective at chopping pike-shafts, or maybe the Landsknecht and Reislaufer mercenaries who wielded them just liked a flamboyant weapon to go with their flamboyant clothing.
As another of my books (”European Swords and Daggers in the Tower of London” - Arthur R. Dufty, Master of the Armouries © 1974) puts it:
With the increased use of water-power, grinding wavy edges onto a straight blade became a lot easier to do than by hand, and far easier than actually forging them that way. I’ve mentioned before, how to tell one from the other is to look at the centreline - is it straight or undulating? Except for one bayonet and one boar-sword, every blade pictured here originally had plain edges.
It’s more likely that so many flamberges survive because they looked different and imposing, going from use on the battlefield to being carried in parades and processions, then - instead of being cut down into something smaller - onto mansion or chateau walls alongside swords made of sawfish snouts and other curiosities, and ultimately into museums.
Some are even more imposing, like this Grossmesser / Zweihänder cross…
Conspicuous consumption is another matter entirely. It’s no accident that most non-Zweihänder flamberge swords look one-off, expensive and impressive.
But not superior in either cut or thrust, or everybody would have wanted and tried to have one.