Possibly the Original Fumble Mechanics
While I'm no role-playing game scholar, Chaosium's Runequest (1978) apparently included fumbles, at least as early as 1980 (which is the Runequest version I just extracted from my shelf and dusted off and whose binding cracked when I flipped through it). It reads
An Adventurer using a weapon for which he has only a 5-20% chance of success has a 5% (a roll of 96-00 on D100) of fumbling. For every additional 20% capability an Adventurer has with a weapon, his chance of fumbling with it is reduced by 1%. However, an attack roll of 00 is always a fumble. Even an Adventurer with a 100% of hitting (actually 95% for dice rolls of 96-00 are always a miss) will fumble if a 00 is rolled. (20)
(It took a moment to find the page number because they're in the outside upper corner of each page.)
A chart on which one is to roll if a fumble occurs appears soon after.
Jon Rees apparently ran these numbers, both for skill use and the chart. I'm looking at Steve Jackson Games' Murphy's Rules (1988), a collection of comic strips detailing amusing and incongruous game rules from the magazines Fantasy Gamer and Space Gamer (yes, there used to be several gaming magazines!), and John Rees submitted an oddity in 1984 that reads
In a 30-minute Runequest battle involving 6,000 armored, experienced warriors using Great Axes, more than 150 men will decapitate themselves and another 600 will chop off their own arms or legs.
So, even then, while the sheer frequency of fumbles wasn't considered necessarily bad design, it was, at least, considered funny.
Speculation: A Possible Reason for Fumbles
Many role-playing gamers view the reality of the role-playing game as a heightened reality, reality-plus, let's call it. In actual reality, very little that happens matters. In reality-plus, everything that happens at the table matters and spectacle is expected, for good or ill. And spectacle during even everyday tasks can lead to comedy or tragedy that is a hallmark of reality-plus.
If, while training with his Great Axe [sic], Argath of Sartar chops off his own head, that's a thing that wouldn't happen in reality, but that spectacle is expected in reality-plus because things happen.
A game with fumbles doesn't mirror reality because the random number generator that's used has so little granularity. A highly trained archer might shoot himself in the head with an arrow or some other absurdity, but that's not gonna happen once per every 100 arrows he fires in actual reality. Were it, archery ranges would be sad, sad places, littered with the dead, naked, and injured.
But in reality-plus if those 100 arrows are fired while they matter launching one of those hundred arrows is likely to cause the archer's armor strap to break or make him fall and twist his ankle (those are average results on the Runequest (1980) Fumble Table). That happens because that's spectacular.
That possibility of spectacle makes the game, for some, more interesting rather than more ridiculous. It turns the game from what some consider a mere boring simulation into a drama, albeit in a really forced way.