What is the Purpose of Catenary Edges?

I'm looking to make a tarp for my hammock because the one I had was torn by the wind in a recent storm, and I've noticed that pretty much every design includes catenary curves at the edges.

I've read that the reason for this is that the curve follows the outline of where the tarp would be taught as opposed to slack if the edges were straight, but i don't understand why this bit of slack is so bad. Why is it so important to remove those sections, as opposed to allowing them to provide some extra cover?