Breaking a dagger in a fight, that's questionable. At other times, breaking a blade can be highly symbolic (I'm thinking of a scene near the end of Hall's
You're Stepping on My Cloak and Dagger).
I should point out that smashing through someone's parry (e.g. parrying a battleaxe with a rapier) is a perfectly reasonable exercise is blade breaking, and I think some weapons were designed for that kind of thing. We're talking here about grabbing a blade and bending it to the point where it either snaps or becomes useless. That's maybe not such a great idea, and it certainly would take strong wrists and fast reflexes.
I'd say that many "sword breakers" are for catching blades, and many are also are for catching clubs and sticks (which, to be honest, is rather easier on the fingers manipulating the dagger). But I'd suggest that
Pratchett's Law of Weapon Design is probably the biggest reason these weapons look the way they do.
My 0.002 cents,
F