I read https://arxiv.org/pdf/math/0412512.pdf and I am left a bit lost: why did Grothendieck develop a theory of fibered categories? It seems like it was pitched as "you want to study functors into the category of categories, but these are complicated (they need to be 'pseudofunctors') and so instead you study fibered categories." But I am still a bit lost -- it seems like everything done with stacks in these notes could be done just as easily with pseudofunctors.
So -- what's the benefit? Where does it save to consider fibered categories instead of pseudofunctors?