Infinity Edge only gives 20% critical strike chance (while still good, the item is very expensive and gives no sustain)
Triforce gives a wide variety of utility (and has a good build path), but is expensive and again gives no sustain.
And as I mentioned, she gets just as much of a power spike from finishing BoRK as other carries finishing TF or IE, except she also has sustain, gets it sooner (it's cheaper), gets a useful active (that combines absurdly well with her passive and ult) and it has a very friendly build path (fall behind rushing IE? All the components are very expensive, it will be very hard to catch up.. Fall behind with BoRK? No problem, there's plenty of cheap build components that are cheap to upgrade as well as giving good benefits.)
For Vayne/others, that Current% hp on-hit is just as good as the critical hit bonus from IE. Why doesn't everyone else do it too? Because they don't scale with early Attack Speed as they do with early Attack Damage.
As you mentioned, Vayne isn't the only one that benefits greatly from rushing it. But she is one of the more problematic users of it. Jinx, Kalista, and many bruisers also get a bigger than average power spike (in terms of damage items) for finishing BoRK early on despite the intended design was for dealing with tanks later on. Not saying there's anything wrong with her building BoRK first (She scales off Attack Speed better early game), but she gets too much for doing (Which is why BoRK may need nerfs before Vayne.)