Using a modern Via Ferrata kit, and with the steel cable and other fixed hardware installed in the most famous Via Ferrata region in the world, it's easy to assume that doing a VF route is well protected. And some modern guidebooks and web pages comment on the quality construction of VF routes, and claim that most in and near the Dolomites have good "protection".
But often on VF routes, and especially in the Dolomites, the protection is illusory, and so . . .
Falling on a VF route is usually a very bad idea. There's a few situations on each route where it's OK, but many more where it will likely result in injury, perhaps serious.
Now serious strong experienced rock-climbers doing a VF in the "normal VF" style are unlikely to fall on a VF route in the Dolomites.
So what's the concern?
First that other persons who "come along with" the serious strong climber on a day's outing might not be so strong. Or even if they're not really going to fall, they easily could think they could, so an experienced climber would be smart to be prepared to at least answer questions about the risk (or even bring along some equipment).
Also a serious climber might get the urge to push their limit a bit by trying a sequence in not-normal VF style, and then might take a fall.
Why VF protection is often illusory gets a bit complicated, so the rest of this post is long . . .
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Two reasons why VF falls are different from roped-climbing falls:
a) They can have a very high "fall factor". Roped climbing falls are normally limited to a "fall factor" of 2, and most are much lower impact. Roped climbers think of a FF 2 fall is very high impact. But a fall using a normal VF kit on a VF route can easily have a Fall Factor much larger than 2. Therefore high impact on equipment (could be damaged or even fail) - (why "home-made" VF rigging could be dangerous). And high impact on climber's spine or pelvis (could be damaged or fail).
b) The pattern of construction of VF routes in the Dolomites started during wartime, and soldiers were supposed to just be tough and strong. And back in World War I, soldiers were expendable. So normal traditional approach to design + installation of the cable for most Dolomites VF routes is mainly to make it good for Aid in getting the climber through each sequence, rather than safety in case the climber actually takes a fall.
The critical installed hardware that determines how far a climber falls is the steel post that attaches the cable to the rock. The carabiner(s) of the Via Ferrata kit attached to the climber's harness slide down the cable until it hits the next lower cable-to-rock attachment post. Sort of like Leading a bolt-protected climbing route, where the rope to the falling Lead climber runs free until it "catches" on a quick-draw attached to the next lower bolt.
Key point: The designer / installers of bolts for a modern roped-climbing route think much + carefully about where to place each bolt, so it will prevent a leader from taking a long fall on one of the harder moves of the route (though the easier moves are often not well protected by a close bolt). But the designers + installers of Dolomites VF routes often gave very little concern to placing the cable-to-rock attachment posts close below the harder moves.
Also in a fall, it's not just a matter of how far you fall, it's what you hit. Again designers (the good ones anyway) of bolt-protected roped-climbing routes do their best to place bolts to prevent the falling Leader from hitting a protruding horn or a flat ledge (though close above a ledge, there's not much to be done) -- while designers of Dolomites VF routes traditionally normally do not concern themselves. Therefore it's likely at many points on many VF routes that a falling climber would hit a rock horn or a ledge (or the protruding rigid steel rod of a cable-to-rock attachment post, a hazard unique to VF routes).