Why do we need cofiltered condition on the index category in the definition of pro-categories?

Let $\mathcal{C}$ be a category. The pro-category pro-$\mathcal{C}$ is defined as (see this nLab page) follows: its objects are diagrams $F: D\to \mathcal{C}$ where $D$ is a small cofiltered category. The Hom set between $F: D\to \mathcal{C}$ and $G: E\to \mathcal{C}$ is given by$$\text{pro-}\mathcal{C}(F,G):=lim_{e\in E}colim_{d\in D}(Fd,Ge).$$

My question is:

Why we need the cofiltered condition on the index category $D$? If we do not require $D$ to be cofitered, what will we lose?