I honestly think Vaynes late game is kind of overblown really. She has a pathetic early game and is still fragile through the entire game. A semi low range as well, without the protection that Graves or other shorter range AD carries have. She can be good, but I just don't see her really bad early game always making up for her late game.
No one has ever claimed Vayne is sturdy or long-range. The reason Vayne's late game carries so hard is 1) massive
burst damage for an AD carry, 2) a portion of that is true damage based on the target's health, meaning she cuts through tanks other carries struggle to kill once they're built up with heaps of health and armor (or, in Kog's case, health and MR), and 3) she's highly maneuverable and almost impossible to outrun.
Vayne explodes almost immediately if you catch her out of position, yes, but she can and will kill just about anyone she catches within a few seconds in the end game. The other carries get very dangerous, but you usually can at least try
to fight them. Not so much with Vayne - if she gets the drop on you, you're just kinda boned.