Why would I use a varistor in an ESD/EMI protection circuit instead of a diode or a resettable fuse?
It is application / situation dependent. If you know that your product will be used by knowledgeable person and interact with only qualified / well designed products, no protection is needed.
On the flip side, if it is to be used in a highly noisy environment (lighting within 1cm, 24x7), or by a redneck who just plug in anything and everything, or highly inductive loads, etc. you may want to have double/triple/quadruple protection.
Without knowing what you are designing for / to, it is hard to tell why you need or wouldn't need certain forms of protection.