I don't know if you consider the Swedish Värja m/1685 a rapier - the Swedish word värja translates as rapier.

A bit over 300 000 Värja m/1685 were produced for the Swedish army, and every man in the Carolean Army (that never fought a battle at odds better than 1:1,2) were equipped with one and they were instrumental in many of the great victories that army carried home.

Rapiers were widely used in battle throughout the renaissance and baroque eras. The Swedish army used rapiers from the late 1500s to the 1750s, when the cavalry started using sabres and the infantry ditched using swords (however, officers continued to use ceremonial rapiers and do up to this day).

Edit: Missed a few words.

Side-Question about Kendo-user's view: Weren't katanas not used on the battlefield unless they couldn't avoid it? My understanding was that, while they are well designed and master-pieces of craftsmanship, the quality of the metal and design lead to blades breaking easily, thus the training of swordsmen to dodge rather than parry. Thus spear and bow were preferred.

Modern fencing is not a simulation of rapier combat anyways. It's a simulation of smallsword fighting.

A rapier is about as heavy as a lighter longsword (which, incidentally, is much lighter than people generally assume, about 1.2kg), while a smallsword weighs about 700 grams. They are used in radically different ways, with the rapier being more focused on single-time counters (attack and defend at the same time) and the smallsword more focused on double-time actions (parry and riposte).

So I wouldn't even consider this argument a valid one.

You can crosspost this question to /r/wma if you want opinions on the martial validity of the rapier in a swordfight.

Edit:
For period sources on rapier combat, here is Gran Simulacro dell'Arte e dell'Uso della Scherma(1610) by Ridolfo Cappoferro.

Not all weapons are battlefield weapons. The classic Italian Rapier is certainly a civilian weapon, whereas heavier swords such as the swedish weapon /u/vonadler is talking about were used in both peacetime and wartime, and carried by both civilians and military.

Knives are rather inefficient battlefield weapons in this day and age, accounting for a small minority of battlefield kills. But they account for a much larger number of civilian homicides. A knife is small and easy to carry, it is a good civilian weapon similar to an Italian rapier.

Handguns are very lethal weapons on both civilian and military fronts, accounting for the majority of homicides and are useful enough to be standard issue for most modern soldiers. They are similar to /u/vonadler's Varja, or what i would call a Cut-and-Thrust Rapier or Sidesword.

Assault rifles are exceptionally effective battlefield weapons but account for only a tiny percentage of civilian deaths. They are similar to a Katana or other weapon of war.

Its an imperfect metaphor, but i hope it gets across the message that all these weapons are very lethal, but that each of them was suited to a particular kind of combat.

There are some excellent responses here, but if I were you I would also head over to /r/wma with this question. There are lots of very knowledgeable people over there together with any number of very convincing videos. The rapier was unequivocally deadly, especially in the hands of a master.

it took me a little bit to realize that you were using a hyphen as a comma.