Vayne having a short-range isn't due to her autoattack range; it's because she has absolutely no abilities which allows her to affect enemies outside of her autoattack range.
Every other ADC may use abilities to affect enemies outside of their autoattack range (with the exception of Tristana and arguably Twitch, who can extend their autoattack range).
This puts Vayne at a disadvantage in lane, since she doesn't have the ability to poke/harass or waveclear using abilities. She has to close the gap to fight (which has is good at), but it means that she has already taken damage before the trade started, putting her at an immediate disadvantage.