# Why do we consider that if initial & final positions are same then displacement of an object is Zero?

I was thinking on a basic high school problem about motion on one axis and came across one of those problem where displacement is zero because final and initial positions are same. My question is that why do we have concept of displacement where we take the shortest path an object takes? it is cause of many problems like if the "displacement" is zero then work done will also be zero (even if there is some distance covered) and this will be irrespective of energy consumed .Why don't we just ditch the idea of a hypothetical shortest path and only consider distances. One of reason i came across was that distance is scalar while velocity is vector I think we can devise a system where we can define if distance is being taken as scalar or vector....(as in if distance is only in straight line then distance will be considered vector else scalar) I know there is something stupid i am missing but motive of this post is to rediscover what that thing is....